{"id":1918,"date":"2026-09-17T13:23:38","date_gmt":"2026-09-17T13:23:38","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=1918"},"modified":"2026-09-17T13:23:39","modified_gmt":"2026-09-17T13:23:39","slug":"lenz-law","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/lenz-law\/","title":{"rendered":"Lenz&#8217;s Law Explained"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\n\nLenz&#8217;s law says that an induced current always flows in the direction whose own magnetic field opposes the change in flux that produced it. It is the minus sign in Faraday&#8217;s law: the rate of flux change fixes the size of the induced EMF, and Lenz&#8217;s law fixes its direction.\n\n<\/p><\/div>\n\n<p>Hold a magnet near a coil of wire and nothing at all happens. Push it towards the coil and a current appears in the wire \u2014 and the magnet starts pushing back, as though the coil had grown a pole to meet it.<\/p>\n\n<p>Pull the magnet away again and every direction reverses, yet the magnet still resists you. That stubbornness is not friction and it is not a coincidence. It is the rule that keeps induction from being a source of free energy, and it is exactly what the minus sign in Faraday&#8217;s law is doing there.<\/p>\n\n<h2>What Is Lenz&#8217;s Law?<\/h2>\n\n<p>Lenz&#8217;s law states that an induced current flows in whichever direction its own magnetic field opposes the change in flux that created it.<\/p>\n\n<p>One word in that sentence carries all the weight: change. The induced current does not oppose the magnetic field. It opposes the <em>change<\/em> in the flux threading the circuit, which is a different claim altogether.<\/p>\n\n<p>A steady field induces nothing, however strong it is. Park the most powerful magnet you own inside a coil and leave it there for a year; the flux through that coil is large and utterly constant, and not one electron is pushed round the loop.<\/p>\n\n<ul>\n<li><strong>The trigger is a change of flux.<\/strong> Magnetic flux is the amount of <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/magnetic-field\/\">magnetic field<\/a> threading the loop, counted with a sign. Move a magnet, rotate the coil, squash it, or vary the field, and the flux changes.<\/li>\n<li><strong>The response always fights the trigger.<\/strong> The induced current makes a field of its own, and that field points whichever way slows the change down: against the existing flux while it grows, along it while it shrinks.<\/li>\n<li><strong>No change means nothing at all.<\/strong> No changing flux, no EMF, no current, no force. This is the single most common slip students make on this topic.<\/li>\n<\/ul>\n\n<p>The rule is named after Heinrich Lenz, who set it out in the 1830s, and it is the direction half of <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electromagnetic-induction\/\">electromagnetic induction<\/a>. Faraday&#8217;s law tells you how big the induced EMF is. Lenz&#8217;s law tells you which way it drives.<\/p>\n\n<p>One housekeeping point before any direction is named. A direction is meaningless without a viewpoint, so every clockwise and anticlockwise on this page is stated as it would look to somebody standing at the right-hand end of the coil&#8217;s axis, looking back along it.<\/p>\n\n<h2>Why Faraday&#8217;s Law Carries a Minus Sign<\/h2>\n\n<p>The minus sign in Faraday&#8217;s law is Lenz&#8217;s law written as algebra, and nothing more. Strip it out and the equation still gives you the right size; it simply stops telling you which way the EMF pushes.<\/p>\n\n<p>Suppose for a moment that the sign were a plus. Push a magnet towards a coil and the induced current would turn the near face into the pole that pulls it in.<\/p>\n\n<p>Watch what happens next. The magnet accelerates, so the flux changes faster, so the current grows, so the pull grows, so the magnet accelerates harder still. Meanwhile the circuit is heating up the whole time, and nothing anywhere is paying for it.<\/p>\n\n<p>That is a perpetual-motion machine, built out of a sign error. The minus sign is what rules it out, which is why Lenz&#8217;s law is usually described as conservation of energy wearing a disguise.<\/p>\n\n<h2>The Lenz&#8217;s Law Formula, and What It Does Not Tell You<\/h2>\n\n<p>Lenz&#8217;s law has no formula of its own. It lives inside Faraday&#8217;s law as a minus sign, so the equation to reach for is Faraday&#8217;s:<\/p>\n\n<div class=\"pf-formula\">\u03b5 = -N d\u03a6\/dt<\/div>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Symbol<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Quantity<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Unit<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Notes<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">\u03b5<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">induced EMF<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">volt (V)<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">its sign says which way the EMF drives current round the loop; drop the sign and you are left with the size alone<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">N<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">number of turns the flux threads<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">none<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">every turn sees the same flux, so the coil links N times it; the product N\u03a6 is called the flux linkage<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">\u03a6<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">magnetic flux through one turn<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">weber (Wb)<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">1 Wb = 1 T\u00b7m<sup>2<\/sup>; the field strength multiplied by the area it threads, counted with a sign against the coil&#8217;s chosen normal<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">d\u03a6\/dt<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">rate of change of that flux<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">Wb\/s<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">the only quantity that drives anything; the value of \u03a6 itself never appears in the equation<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">the minus sign<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">Lenz&#8217;s law<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">none<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">the induced EMF acts against the change in flux, never against the flux itself<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Signs only mean something once you have fixed a convention, so here is the one used throughout this page. Take the axis positive to the right, let that be the coil&#8217;s positive normal, and call a current positive when it runs anticlockwise as seen from the right-hand end. A negative EMF then means a clockwise drive.<\/p>\n\n<p>If you already know a flux change and how long it took, the arithmetic is short, and our <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/faradays-law\">Faraday&#8217;s law calculator<\/a> will do it for you: it takes a uniform field changing over a flat area, so that the flux change is the area multiplied by the field change, and solves for the EMF, the turns, the area, the field change or the time. What it hands back is a <em>size<\/em>. The sign it leaves off is precisely what Lenz&#8217;s law supplies, and the lab below is where you can watch that sign behave. Our <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/faradays-law-formula\/\">Faraday&#8217;s law formula<\/a> guide takes the algebra of the size apart separately.<\/p>\n\n<p>That lab puts a magnet on the axis of a coil and hands you the controls: where the magnet sits, how fast and which way it moves, how many turns the coil carries and what resistance the circuit presents. A button turns the magnet end for end.<\/p>\n\n<p>Two behaviours are worth hunting for deliberately. Drop the resistance and the current, the force and the heat all climb while the EMF does not budge. Slide the magnet to the coil&#8217;s exact centre and the EMF collapses to zero at the very moment the flux is largest. Watch the readouts rather than the drawing while you do that: the force arrow under the magnet is not drawn to scale, since its length grows as sqrt(force) from a fixed minimum stub, whereas the motion arrow above it does follow the speed.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Lenz&#039;s Law Lab<\/span><\/div><div class=\"pf-sim-slot-body\"><style>.pf-sim-frame{width:100%;border:none;height:600px}@media(max-width:760px){.pf-sim-frame{height:1000px}}<\/style><iframe src=\"\/labs\/lenz-law.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>How to Find the Direction in Three Steps<\/h2>\n\n<p>Finding the direction of an induced current takes three steps, and they work for any change of flux, not only for a magnet on the move.<\/p>\n\n<ol>\n<li><strong>Work out which way the existing flux points through the coil, and whether it is growing or shrinking.<\/strong> A magnet&#8217;s field leaves its north end, so a north end pointing right sends flux rightwards through a coil in front of it. Closing on the coil makes that flux grow; retreating makes it shrink.<\/li>\n<li><strong>Point the induced field the opposite way to the change.<\/strong> If the flux is growing, the induced current&#8217;s own field inside the coil points against it. If the flux is shrinking, the induced field points along it, propping the flux up.<\/li>\n<li><strong>Curl your right hand round the coil with your thumb along that induced field.<\/strong> Your fingers now run the way the current runs. Say which end you are looking from, and you have a direction somebody else can check.<\/li>\n<\/ol>\n\n<p>Notice that step two never mentions the magnet. It only asks what the flux is doing. That is why the same three steps handle a coil being rotated, a switch being opened in a neighbouring circuit, or a field that is simply being turned up.<\/p>\n\n<figure style=\"margin:32px auto;max-width:720px;text-align:center;\">\n  <img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/lenz-law-diagram-01-768x660.jpg\" srcset=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/lenz-law-diagram-01-768x660.jpg 768w, https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/lenz-law-diagram-01.jpg 1240w\" sizes=\"auto, (max-width: 760px) 100vw, 720px\" width=\"1240\" height=\"1066\" alt=\"Four panels showing Lenz's law for a bar magnet on the axis of a coil, with the magnet on the left of the coil in every panel. Panel 1, north end leading and pushed in: the flux through the coil points right and is growing, the induced current runs clockwise seen from the right, the coil's near face is a north pole and the force repels the magnet. Panel 2, north end leading and pulled out: the flux points right and is shrinking, the current runs anticlockwise, the near face is a south pole and the force attracts the magnet. Panel 3, south end leading and pushed in: the flux points left and is growing, the current runs anticlockwise, the near face is a south pole and the force repels. Panel 4, south end leading and pulled out: the flux points left and is shrinking, the current runs clockwise, the near face is a north pole and the force attracts. Each panel draws the magnet with its north half dark red and its south half pale, a motion arrow above it, a force arrow below it pointing the opposite way, and a small end-on inset showing the current's sense as seen from the right. A dark band across the foot reads: reverse the motion or flip the magnet and every direction reverses, the force never does, it always opposes the motion.\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;border-radius:4px;\">\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">The four cases of Lenz&#8217;s law, with the magnet approaching or leaving from the left of the coil. Reverse the motion or turn the magnet round and every direction reverses; the force never does.<\/figcaption>\n<\/figure>\n\n<p>Those four cases are worth learning as a set, because they are the whole law. Two of them repel and two attract, and in every one of them the force points against the motion.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Magnet end leading<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Motion<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Flux through the coil<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Induced current, seen from the right<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Coil&#8217;s near face<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Force on the magnet<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">north<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">towards the coil<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">points right, growing<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">clockwise<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">north pole<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">repels: pushes it back out<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">north<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">away from the coil<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">points right, shrinking<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">anticlockwise<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">south pole<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">attracts: pulls it back in<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">south<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">towards the coil<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">points left, growing<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">anticlockwise<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">south pole<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">repels: pushes it back out<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">south<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">away from the coil<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">points left, shrinking<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">clockwise<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">north pole<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">attracts: pulls it back in<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Read the last two columns together and the pattern lands. The coil always presents the magnet with the face it least wants to see: a matching pole while the magnet closes in, an opposite pole while it leaves.<\/p>\n\n\n<h2>What Happens as a Magnet Goes Through a Coil<\/h2>\n\n<p>As a magnet travels along a coil&#8217;s axis the induced EMF starts small, climbs to a peak before the magnet arrives, collapses to exactly zero as it passes the centre, then climbs to an equal and opposite peak on the way out.<\/p>\n\n<p>Every number that follows comes from one deliberately simple model, and it is worth stating plainly what that model is. Picture 200 coincident circular turns of radius 20.0 mm. The magnet is a point dipole of moment 1.00 A\u00b7m<sup>2<\/sup> travelling along the axis, and the circuit is a pure resistance of 10.0 \u03a9.<\/p>\n\n<p>The 20.0 mm radius and the 1.00 A\u00b7m<sup>2<\/sup> moment are a chosen scale, not measurements of any real coil or magnet. Treat every number on this page as a number for this model.<\/p>\n\n<p>The model has real edges, and they are easy to state. A bar magnet is not a point dipole, so within roughly its own length of the coil, and inside it, the true flux departs from the formula below. The turns are treated as sitting at one place, while a real coil has length. And a real circuit has self-inductance, which delays and reduces the current at high speed; this model ignores it.<\/p>\n\n<div class=\"pf-formula\">\u03a6(z) = \u03bc<sub>0<\/sub> m a<sup>2<\/sup> \/ (2 (z<sup>2<\/sup> + a<sup>2<\/sup>)<sup>3\/2<\/sup>)<\/div>\n\n<p>Here z is the magnet&#8217;s position measured from the coil centre, a is the coil radius, m is the dipole moment, and \u03bc<sub>0<\/sub> is the magnetic constant, 4\u03c0 \u00d7 10<sup>-7<\/sup> T\u00b7m\/A. Since the 2019 revision of the SI that constant is a measured quantity rather than a defined one, but it departs from 4\u03c0 \u00d7 10<sup>-7<\/sup> only around the tenth significant figure \u2014 far below anything printed here. The measured figure is published by <a href=\"https:\/\/physics.nist.gov\/cgi-bin\/cuu\/Value?mu0\" target=\"_blank\" rel=\"noopener\">NIST as the vacuum magnetic permeability<\/a>.<\/p>\n\n<p>Everything else follows from one quantity: S = d(N\u03a6)\/dz, the slope of the flux linkage with the magnet&#8217;s position, measured in webers per metre. Three short lines then give the whole story.<\/p>\n\n<div class=\"pf-formula\">\u03b5 = -S v &nbsp;\u00b7&nbsp; I = \u03b5\/R &nbsp;\u00b7&nbsp; F = I S = -S<sup>2<\/sup> v \/ R<\/div>\n\n<p>The last of those three is Lenz&#8217;s law in one glance. The force carries S squared, so it cannot care about the sign of S, and it carries a bare minus in front of v. Whichever way the magnet moves, the force points the other way.<\/p>\n\n<p>The current comes straight from <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/ohms-law\/\">Ohm&#8217;s law<\/a>, which is why the resistance changes the current and the force without touching the EMF at all. The EMF is made by the moving flux; the resistance only decides how much current that EMF manages to drive.<\/p>\n\n<figure style=\"margin:32px auto;max-width:720px;text-align:center;\">\n  <img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/lenz-law-diagram-02-768x616.jpg\" srcset=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/lenz-law-diagram-02-768x616.jpg 768w, https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/lenz-law-diagram-02.jpg 1240w\" sizes=\"auto, (max-width: 760px) 100vw, 720px\" width=\"1240\" height=\"994\" alt=\"Two stacked graphs sharing one horizontal axis, the magnet's position from minus 60 to plus 60 millimetres from the coil centre. The upper graph is the flux linkage through a 200-turn coil in milliwebers, from 0 to 7, and is a single gold hump that peaks at the coil centre: a ringed point marks 6.2832 milliwebers at the centre and another marks 4.4959 milliwebers at minus 10 millimetres. The lower graph is the induced EMF in millivolts, from minus 300 to plus 300, and is an S-shaped gold curve that passes through zero exactly at the coil centre: ringed points mark minus 269.75 millivolts at minus 10 millimetres, 0.00 millivolts at the centre, and 269.75 millivolts at plus 10 millimetres. Dotted vertical lines at minus 10, 0 and plus 10 millimetres run through both graphs, labelled peak, coil centre and peak. The EMF curve is largest exactly where the linkage curve is steepest, and zero where the linkage curve is flat at its maximum.\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;border-radius:4px;\">\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">Flux linkage through the 200-turn coil and the EMF it induces, for the point dipole moving right at 1.0 m\/s. The EMF is minus the slope of the upper curve multiplied by the speed, which is why it hits zero exactly where the linkage is largest and peaks 10 mm either side of the centre.<\/figcaption>\n<\/figure>\n\n<p>Two features of that picture come out of the algebra rather than the arithmetic. The slope S carries a factor of z, so it vanishes exactly at the centre; and the size of S peaks at exactly half a coil radius, which for this 20.0 mm coil puts the two EMF peaks at 10.0 mm either side.<\/p>\n\n<div class=\"pf-table-scroll\" style=\"display:block;width:100%;max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;margin:1.5em 0;\">\n<table style=\"width:100%;border-collapse:collapse;word-break:break-word;\">\n<thead>\n<tr>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Position z (mm)<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Flux per turn (\u00b5Wb)<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Slope S (Wb\/m)<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">EMF (mV)<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Current (mA)<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">Force (mN)<\/th>\n<th style=\"text-align:left;padding:8px;border-bottom:2px solid #D9CFB8;\">What the force does<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-60<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.993<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.0089411<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-8.94<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-0.89<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.007994<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">repels<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-40<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">2.810<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.033719<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-33.72<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-3.37<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.1137<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">repels<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-20<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">11.107<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.16661<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-166.61<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-16.66<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">2.776<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">repels<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-10<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">22.479<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.26975<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-269.75<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-26.98<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">7.277<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">repels, hardest here<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">31.416<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.00<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.00<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">nothing at all<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">+10<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">22.479<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-0.26975<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">269.75<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">26.98<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">7.277<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">attracts, hardest here<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">+20<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">11.107<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-0.16661<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">166.61<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">16.66<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">2.776<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">attracts<\/td><\/tr>\n<tr><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">+60<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.993<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">-0.0089411<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">8.94<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.89<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">0.007994<\/td><td style=\"padding:8px;border-bottom:1px solid #D9CFB8;\">attracts<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Every figure in that table is rounded for display, at N = 200, R = 10.0 \u03a9 and v = 1.0 m\/s with the north end pointing right. Work out ratios from the formulae rather than by dividing two rounded entries, which is a habit that quietly costs marks.<\/p>\n\n<p>The last column is the honest headline. On the way in the magnet is pushed back; on the way out it is pulled back; at the centre it is left alone for an instant. The one thing that never happens is a shove in the direction it was already going.<\/p>\n\n<h2>Why Lenz&#8217;s Law Is Really Energy Conservation<\/h2>\n\n<p>Lenz&#8217;s law is not a separate law of nature. It is conservation of energy turning up as a sign, and in this model the two sums agree to the last digit the arithmetic can carry.<\/p>\n\n<p>Take the default push: the magnet 10 mm short of the 200-turn coil, closing at 1.0 m\/s. The mechanical power you supply against the induced force is 7.27666 mW, and the electrical power dissipated in the 10.0 \u03a9 circuit is 7.27666 mW.<\/p>\n\n<p>Those two numbers arrive by different routes. One is force multiplied by velocity; the other is current squared multiplied by resistance. They come out identical because the algebra makes them identical, not because they were tuned to match.<\/p>\n\n<figure style=\"margin:32px auto;max-width:720px;text-align:center;\">\n  <img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/lenz-law-diagram-03-768x374.jpg\" srcset=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/lenz-law-diagram-03-768x374.jpg 768w, https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/lenz-law-diagram-03.jpg 1240w\" sizes=\"auto, (max-width: 760px) 100vw, 720px\" width=\"1240\" height=\"604\" alt=\"A bar chart with two horizontal bars drawn to the same scale from 0 to 8 milliwatts, with ticks every 2 milliwatts. The upper gold bar, labelled mechanical power you put in, reaches 7.27666 milliwatts. The lower dark red bar, labelled electrical power out as heat, reaches 7.27666 milliwatts. Both bars are exactly the same length because the two numbers are equal. A dark band beneath reads: the two numbers are computed by different routes and come out identical, and that identity is the minus sign.\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;border-radius:4px;\">\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">The energy account for the default push. The bars are the same length because the two numbers are equal, which is the whole content of the minus sign.<\/figcaption>\n<\/figure>\n\n<p>Push the magnet the full way through, from 60 mm out to 60 mm past at a steady 1.0 m\/s, and the work done against the induced force is 217.859 \u00b5J. That figure is a numerical integral along the path rather than a single reading, and the pass takes 0.120 s, so the average electrical power is 1.8155 mW.<\/p>\n\n<p>That is a tiny amount of energy, and this page will not pretend otherwise. The point is not that it is large; the point is that it is not zero, and that it came out of your arm.<\/p>\n\n<p>This is also why a generator gets harder to turn the instant somebody switches a lamp on. With the switch open there is an EMF and no current at all, so nothing but friction opposes the rotation. Close the switch, current flows, the induced forces appear, and the extra effort at the handle is what pays for the light.<\/p>\n\n<h2>Where You Meet Lenz&#8217;s Law Every Day<\/h2>\n\n<p>Lenz&#8217;s law shows up wherever a conductor and a changing magnetic field share a room, and most of the time it is felt as unexpected resistance rather than seen as a current.<\/p>\n\n<ul>\n<li><strong>A bicycle dynamo.<\/strong> Switch the lamp on and the wheel becomes measurably harder to turn. Nothing has touched the wheel; the load simply let current flow, and the induced forces did the rest.<\/li>\n<li><strong>Magnetic braking.<\/strong> Trains, roller-coasters and gym flywheels are slowed by dragging a conductor past a magnet. The braking force appears only while there is relative motion, which is why these brakes fade smoothly to nothing rather than locking.<\/li>\n<li><strong>Induction hobs and metal detectors.<\/strong> Both drive a rapidly changing field into a conductor and rely on the currents it induces \u2014 one to heat a pan, the other to give away a buried coin.<\/li>\n<li><strong>Moving-coil meters.<\/strong> The needle settles instead of swinging for a minute, because its own motion induces a current that opposes that motion.<\/li>\n<li><strong>An <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electromagnet\/\">electromagnet<\/a> being switched off.<\/strong> The collapsing flux induces an EMF that tries to keep the current going, which is why coils spark at a switch and why a diode is often fitted across them.<\/li>\n<\/ul>\n\n<p>It even reaches national infrastructure. A geomagnetic storm makes the Earth&#8217;s field vary, that varying flux threads the enormous circuit formed by a power grid, and real current flows in the lines, running the way Lenz&#8217;s law says it must; the NOAA Space Weather Prediction Center describes the consequences for <a href=\"https:\/\/www.swpc.noaa.gov\/impacts\/electric-power-transmission\" target=\"_blank\" rel=\"noopener\">electric power transmission<\/a>.<\/p>\n\n<p>The famous classroom demonstration belongs here too, with one caveat. A magnet dropped down a copper pipe drifts down far more slowly than it has any right to, and the principle is exactly the one on this page. The difference is that the currents circulate inside the bulk metal rather than round a wire loop, which makes it a question about eddy currents; it gets its own article rather than a number here.<\/p>\n\n<figure style=\"margin:32px auto;max-width:640px;text-align:center;\">\n  <img decoding=\"async\" src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/09\/a-bicycle-dynamo-on-a-wheel.jpg\"\n       alt=\"Bicycle bottle dynamo pressed against a wheel, an everyday example of Lenz's law making the wheel harder to turn\"\n       loading=\"lazy\"\n       style=\"width:100%;height:auto;border-radius:4px;\" width=\"1920\" height=\"1440\">\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">A bottle dynamo on a bicycle wheel. Switching the lamp on lets current flow, and Lenz&#8217;s law turns that current into a drag you can feel in your legs.<\/figcaption>\n<\/figure>\n\n<h2>Common Misconceptions About Lenz&#8217;s Law<\/h2>\n\n<p>Four beliefs account for most of the marks lost on this topic, and every one of them can be tested against the lab above in under a minute.<\/p>\n\n<ul>\n<li><strong>&#8220;The induced current opposes the magnetic field.&#8221;<\/strong> It opposes the <em>change<\/em> in flux. A field as strong as you like, held steady, induces absolutely nothing; a feeble field that is changing quickly induces plenty.<\/li>\n<li><strong>&#8220;The force is always a repulsion.&#8221;<\/strong> Only while the magnet is closing in. Pull it away and the coil attracts it instead. What stays constant is not the sense of the force but its relationship to the motion: it always opposes it.<\/li>\n<li><strong>&#8220;Turning the magnet round makes it easier or harder to push.&#8221;<\/strong> It makes no difference whatever. Flipping the magnet reverses the flux, the EMF and the current, and leaves the force on the magnet exactly where it was, because the force depends on the square of the linkage slope.<\/li>\n<li><strong>&#8220;The flux is biggest at the centre, so the EMF must be too.&#8221;<\/strong> Precisely backwards. The EMF follows the slope of the flux linkage, and a hump is flattest at its summit, so the EMF is zero exactly where the flux is greatest.<\/li>\n<\/ul>\n\n<p>There is a fifth worth adding, because it is a reading error rather than a physics error. Lenz&#8217;s law does not give you the size of an induced EMF; Faraday&#8217;s law does. Asking Lenz&#8217;s law how many millivolts you will get is like asking a compass how far away the town is.<\/p>\n\n<h2>Worked Problems<\/h2>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 1<\/div><div class=\"pf-problem-question\">A coil of 200 turns and radius 20.0 mm sits in a circuit of total resistance 10.0 ohm. A magnet modelled as a point dipole of moment 1.00 A m^2 lies on the axis 10.0 mm to the left of the coil centre with its north end pointing right, moving towards the coil at 1.0 m\/s. Find the flux per turn, the induced EMF, the current and its direction, and the force on the magnet.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Five short lines do the whole job. The flux through one turn is \u03a6 = \u03bc<sub>0<\/sub> m a<sup>2<\/sup> \/ (2 (z<sup>2<\/sup> + a<sup>2<\/sup>)<sup>3\/2<\/sup>), the slope of the flux linkage is S = d(N\u03a6)\/dz, and then \u03b5 = -S v, I = \u03b5\/R and F = I S.\n\nStep 2: Substitute the geometry. z = -0.010 m and a = 0.020 m, so z<sup>2<\/sup> + a<sup>2<\/sup> = 0.000100 + 0.000400 = 0.000500 m<sup>2<\/sup>, giving \u03a6 = 22.4794 \u00b5Wb per turn and a flux linkage N\u03a6 = 4.49588 mWb. Differentiating gives S = 0.2697529 Wb\/m.\n\nStep 3: \u03b5 = -S v = -(0.2697529 Wb\/m) \u00d7 (1.0 m\/s) = -0.2697529 V, which is -269.7529 mV.\n\nStep 4: I = \u03b5\/R = -0.2697529 V \/ 10.0 \u03a9 = -0.02697529 A, which is -26.9753 mA. The minus sign means clockwise as seen from the right-hand end of the axis.\n\nStep 5: F = I S = (-0.02697529 A) \u00d7 (0.2697529 Wb\/m) = -0.00727666 N. The minus sign puts the force along the negative axis, pointing away from the coil.\n\n<strong>Answer: -269.7529 mV, driving 26.9753 mA clockwise seen from the right, with a force of 7.27666 mN pushing the magnet back.<\/strong> The coil&#8217;s near face has become a north pole, meeting the magnet&#8217;s north end with a repulsion. You have to work to keep the magnet moving.\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">Take the same magnet at the same place, 10.0 mm to the left of the coil with its north end pointing right, but now pull it away from the coil at 1.0 m\/s instead of pushing it in. What changes, and what does not?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Nothing about the geometry has moved, so the flux and its slope are untouched: \u03a6 = 22.4794 \u00b5Wb per turn and S = 0.2697529 Wb\/m, exactly as before. Only v has changed sign, to -1.0 m\/s.\n\nStep 2: \u03b5 = -S v = -(0.2697529 Wb\/m) \u00d7 (-1.0 m\/s) = +0.2697529 V, which is +269.7529 mV. Every sign in the electrical story has flipped.\n\nStep 3: I = \u03b5\/R = +0.2697529 V \/ 10.0 \u03a9 = +0.02697529 A, which is +26.9753 mA, now anticlockwise seen from the right. The coil&#8217;s near face is a south pole.\n\nStep 4: F = I S = (+0.02697529 A) \u00d7 (0.2697529 Wb\/m) = +0.00727666 N. The force now points along the positive axis, towards the coil.\n\n<strong>Answer: the EMF, the current, the induced pole and the direction of the force all reverse, and the size of the force is identical at 7.27666 mN.<\/strong> Approaching, the coil pushed the magnet away; retreating, it pulls the magnet back. Either way it is slowed, and either way you are the one doing the work.\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">The same magnet is now exactly at the coil centre, z = 0, still travelling at 1.0 m\/s with 200 turns and a 10.0 ohm circuit. The flux through the coil has never been larger. How big is the induced EMF?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Put z = 0 into the flux formula. z<sup>2<\/sup> + a<sup>2<\/sup> = 0 + 0.000400 = 0.000400 m<sup>2<\/sup>, which gives \u03a6 = 31.4159 \u00b5Wb per turn and a flux linkage N\u03a6 = 6.28319 mWb. That is the largest flux anywhere on the axis.\n\nStep 2: Now look at the slope. Differentiating the flux formula puts a factor of z in the numerator of S, so S = 0 exactly when z = 0, no matter how large the flux is.\n\nStep 3: \u03b5 = -S v = 0 \u00d7 1.0 = 0 V, so I = 0 A and F = I S = 0 N.\n\n<strong>Answer: the EMF is exactly zero, and so are the current and the force, at the very position where the flux is greatest.<\/strong> Faraday&#8217;s law reads the rate of change, not the amount. The magnet is momentarily at the summit of the flux hump, and a summit is flat.\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">Rewind to the first problem, but wind 300 turns on the coil instead of 200. Everything else is unchanged: z = -10.0 mm, v = 1.0 m\/s, R = 10.0 ohm. By how much do the EMF and the force grow?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: The flux through one turn does not depend on N at all, so it stays at 22.4794 \u00b5Wb. The linkage does: N\u03a6 = 6.74382 mWb with 300 turns.\n\nStep 2: S is proportional to N, so recomputing it at N = 300 gives S = 0.4046293 Wb\/m. Then \u03b5 = -S v = -0.4046293 V, which is -404.6293 mV, and I = \u03b5\/R = -0.04046293 A, which is -40.4629 mA.\n\nStep 3: F = I S = (-0.04046293 A) \u00d7 (0.4046293 Wb\/m) = -0.0163725 N, a force of 16.3725 mN.\n\nStep 4: Get the growth factors from the formulae, not from the numbers. Since \u03b5 = -S v and S is proportional to N, the EMF scales as N: the factor is exactly 300\/200 = 1.5. Since F = -S<sup>2<\/sup> v \/ R, the force scales as N squared: the factor is exactly (300\/200)<sup>2<\/sup> = 2.25, and 7.27666 mN \u00d7 2.25 = 16.3725 mN.\n\n<strong>Answer: the EMF rises by exactly 1.5 times and the force by exactly 2.25 times.<\/strong> Here is the trap. Round both forces to three significant figures first, to 7.28 mN and 16.4 mN, and their quotient is 2.2527, not 2.25. Take ratios from the algebra, never from two rounded readings.\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">Back to 200 turns, with the magnet at z = -10.0 mm moving in at 1.0 m\/s. Swap the 10.0 ohm circuit for a 1.0 ohm one. What happens to the EMF, the current, the force and the heat?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: The EMF is made by the changing flux and knows nothing about the circuit. S is still 0.2697529 Wb\/m, so \u03b5 = -S v = -0.2697529 V, which is -269.7529 mV. Unchanged.\n\nStep 2: I = \u03b5\/R = -0.2697529 V \/ 1.0 \u03a9 = -0.2697529 A, which is -269.753 mA. Against the 26.9753 mA of the 10.0 \u03a9 case, that is ten times the current: 26.9753 \u00d7 10 = 269.753.\n\nStep 3: F = I S = (-0.2697529 A) \u00d7 (0.2697529 Wb\/m) = -0.0727666 N, a force of 72.7666 mN. Again ten times the original, since 7.27666 \u00d7 10 = 72.7666.\n\nStep 4: The heat is P = I<sup>2<\/sup>R = (0.2697529 A)<sup>2<\/sup> \u00d7 1.0 \u03a9 = 0.0727666 W, which is 72.7666 mW, also ten times the 7.27666 mW of the first problem.\n\n<strong>Answer: the EMF does not move at all; the current, the force and the heat all rise by a factor of ten.<\/strong> The load is what decides how hard the magnet is to push. An open circuit gives you an EMF and no force whatsoever, which is the generator with its lamp switched off.\n\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">Turn the magnet end for end so its south end now points right, and push it in from z = -10.0 mm at 1.0 m\/s with 200 turns and a 10.0 ohm circuit. Which quantities reverse, and does the magnet become easier to push?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n\n<strong>Solution:<\/strong>\n\nStep 1: Flipping the magnet reverses its dipole moment to m = -1.00 A\u00b7m<sup>2<\/sup>. The flux reverses with it: \u03a6 = -22.4794 \u00b5Wb per turn, N\u03a6 = -4.49588 mWb, and S = -0.2697529 Wb\/m.\n\nStep 2: \u03b5 = -S v = -(-0.2697529 Wb\/m) \u00d7 (1.0 m\/s) = +0.2697529 V, which is +269.7529 mV, and I = \u03b5\/R = +0.02697529 A, which is +26.9753 mA, anticlockwise seen from the right.\n\nStep 3: F = I S = (+0.02697529 A) \u00d7 (-0.2697529 Wb\/m) = -0.00727666 N, a force of 7.27666 mN pointing away from the coil. Exactly the value of the first problem.\n\nStep 4: The reason is in the formula. F = -S<sup>2<\/sup> v \/ R contains the square of S, so reversing the sign of S cannot touch the force. Only the sign of v decides which way the force points.\n\n<strong>Answer: the flux, the EMF, the current and the induced pole all reverse; the force is unchanged at 7.27666 mN and still repels.<\/strong> The coil now presents a south face to a south end, which repels just as firmly as north against north. The magnet is exactly as hard to push as before.\n\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What is Lenz&#039;s law in simple terms?<\/summary><div class=\"pf-faq-item-answer\">\n\nAn induced current always flows the way that fights whatever caused it. If a magnet is coming closer, the coil turns the face nearest the magnet into a matching pole and pushes it away. If the magnet is leaving, the coil turns that same face into an opposite pole and pulls it back. Either way the coil resists the change.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why is there a minus sign in Faraday&#039;s law?<\/summary><div class=\"pf-faq-item-answer\">\n\nThe minus sign is Lenz&#8217;s law. It records that the induced EMF acts against the change in flux rather than with it. Without it the equation would allow a magnet to be pulled in faster and faster while the circuit heated up, with no energy source anywhere. The sign is conservation of energy written into the formula.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>How do you find the direction of an induced current?<\/summary><div class=\"pf-faq-item-answer\">\n\nWork out which way the flux through the coil points and whether it is growing or shrinking. Give the induced field the opposite job: against the flux if it is growing, along it if it is shrinking. Then curl your right hand round the coil with the thumb along that induced field, and your fingers give the current&#8217;s direction.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Is Lenz&#039;s law the same as Faraday&#039;s law?<\/summary><div class=\"pf-faq-item-answer\">\n\nNo. Faraday&#8217;s law gives the size of an induced EMF from how fast the flux linkage changes. Lenz&#8217;s law gives the direction, and it is the reason Faraday&#8217;s equation carries a minus sign. You need both: one tells you how many volts, the other tells you which way round the circuit they drive.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Does Lenz&#039;s law break conservation of energy?<\/summary><div class=\"pf-faq-item-answer\">\n\nIt is the opposite: Lenz&#8217;s law exists because energy is conserved. In the model on this page the mechanical power supplied against the induced force and the electrical power dissipated in the circuit are identical by algebra, not by coincidence. Reverse the direction rule and you would get current, heat and acceleration from nothing at all.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Does Lenz&#039;s law apply if the magnet is not moving?<\/summary><div class=\"pf-faq-item-answer\">\n\nNothing is induced by a stationary magnet, however strong it is. Lenz&#8217;s law and Faraday&#8217;s law both respond to the rate of change of flux, and a magnet at rest changes nothing. Hold a magnet inside a coil for an hour and the flux is large and constant, the EMF is zero, and no current flows at any point.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why does a magnet fall slowly down a copper pipe?<\/summary><div class=\"pf-faq-item-answer\">\n\nBecause the falling magnet changes the flux through each ring of the pipe wall, currents are induced there, and by Lenz&#8217;s law they oppose the motion that made them. The principle is the one on this page, but the currents swirl inside solid metal rather than round a wire loop, so the topic is properly eddy currents.\n\n<\/div><\/details>\n","protected":false},"excerpt":{"rendered":"<p>Lenz&#8217;s law says an induced current always flows the way that opposes the change in flux that produced it, which is the minus sign in Faraday&#8217;s law EMF = -N dPhi\/dt. The three-step direction rule, the four cases, why the EMF is zero where the flux is largest, the energy argument, six worked problems and an interactive lab.<\/p>\n","protected":false},"author":1,"featured_media":1922,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-1918","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-electromagnetism"],"_links":{"self":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/1918","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/comments?post=1918"}],"version-history":[{"count":3,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/1918\/revisions"}],"predecessor-version":[{"id":1995,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/1918\/revisions\/1995"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/1922"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=1918"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=1918"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=1918"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}