{"id":819,"date":"2026-08-14T23:57:39","date_gmt":"2026-08-14T23:57:39","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=819"},"modified":"2026-08-24T13:03:39","modified_gmt":"2026-08-24T13:03:39","slug":"electromagnet","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electromagnet\/","title":{"rendered":"Electromagnets: How They Work"},"content":{"rendered":"\n<div class=\"pf-citation\"><div class=\"eyebrow\">Definition<\/div><p>\n\nAn electromagnet is a magnet created by electric current: current flowing through a coil of wire produces a magnetic field, and an iron core inside the coil multiplies that field many times over. Its strength follows B equals the permeability times turns per metre times current, and it switches off the instant the current does.\n\n<\/p><\/div>\n\n<p>Somewhere within a few metres of you right now, a coil of wire is pretending to be a magnet. It is in the little speaker in your phone, in the motor that spins your fan, in the doorbell nobody has rung in weeks.<\/p>\n\n<p>What makes these coils remarkable is not that they are strong. It is that they are <em>obedient<\/em>. Cut the current and the magnetism vanishes \u2014 which is precisely why a scrapyard crane can pick up a car and then, at the flick of a switch, drop it.<\/p>\n\n<h2>What Is an Electromagnet?<\/h2>\n\n<p>An electromagnet is a device that becomes magnetic only while an electric current flows through it. In its simplest form it is nothing more than a coil of insulated wire, usually wound around a core of soft iron.<\/p>\n\n<p>The physics underneath is a single, sweeping fact: <strong>every electric current produces a magnetic field around itself<\/strong>. A straight wire makes a weak field that circles around it. Coil that same wire into a tight helix \u2014 a <em>solenoid<\/em> \u2014 and the loops stack their fields together into something strong and orderly down the middle.<\/p>\n\n<p>Add an iron core and the field can leap by a factor of hundreds. That combination, coil plus core plus current, is what almost everyone means by &#8220;electromagnet&#8221;.<\/p>\n\n<figure class=\"pf-figure\" style=\"margin:1.6em 0;\"><img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/electromagnet-wire-coil-wound-around-soft.webp\" width=\"1440\" height=\"846\" alt=\"Electromagnet diagram: a wire coil wound around a soft iron core and connected to a DC supply, with magnetic field lines looping from the north pole around to the south pole\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;max-width:720px;display:block;margin:0 auto;\" \/><\/figure>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;margin-top:4px;\">Inside the core the field runs left to right; outside it loops back from N to S. To find which end is north, curl the fingers of your right hand around the coil in the direction of conventional current \u2014 your thumb points to the north pole.<\/p>\n\n<h3>The Two Ingredients<\/h3>\n\n<ul>\n<li><strong>The coil<\/strong> \u2014 many turns of insulated wire. Insulation matters: bare wire would short across neighbouring turns and the current would take the shortcut instead of going round.<\/li>\n<li><strong>The core<\/strong> \u2014 a ferromagnetic material, almost always soft iron. &#8220;Soft&#8221; here is magnetic, not mechanical: it magnetises easily and, crucially, lets go again.<\/li>\n<\/ul>\n\n<p>William Sturgeon built the first practical electromagnet in the 1820s. Joseph Henry then made far stronger ones by insulating the wire, which let him wind many close-packed turns without shorting \u2014 the same trick every coil still uses today.<\/p>\n\n<h2>The Electromagnet Formula<\/h2>\n\n<p>The magnetic field inside a long, tightly wound coil is given by a formula clean enough to memorise in one sitting.<\/p>\n\n<div class=\"pf-formula\">B = \u03bc<sub>0<\/sub> n I (air-cored coil)<\/div>\n\n<p>With a ferromagnetic core in place, the core&#8217;s relative permeability multiplies the result:<\/p>\n\n<div class=\"pf-formula\">B = \u03bc<sub>r<\/sub> \u03bc<sub>0<\/sub> n I (where n = N \/ L)<\/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;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Symbol<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Quantity<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">SI unit<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>B<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Magnetic flux density inside the coil<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">tesla (T)<\/td><\/tr>\n<tr style=\"background:#F5F2EA;\"><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>\u03bc<sub>0<\/sub><\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Permeability of free space, 4\u03c0 \u00d7 10<sup>\u22127<\/sup><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">T\u00b7m\/A (same as N\/A<sup>2<\/sup>)<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>\u03bc<sub>r<\/sub><\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Relative permeability of the core (air = 1)<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">no units<\/td><\/tr>\n<tr style=\"background:#F5F2EA;\"><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>n<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Turns per unit length<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">turns per metre (m<sup>\u22121<\/sup>)<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>N<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Total number of turns<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">no units<\/td><\/tr>\n<tr style=\"background:#F5F2EA;\"><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>L<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Length of the coil<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">metre (m)<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\"><strong>I<\/strong><\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Current through the coil<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">ampere (A)<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Two features of this equation surprise people. There is no radius in it \u2014 a fat coil and a thin coil with the same turns density give the same internal field. And there is no <em>N<\/em> on its own, only <em>N<\/em> divided by <em>L<\/em>.<\/p>\n\n<p>That second point is the single most common source of wrong answers, so it is worth saying plainly: <strong>the field depends on turns per metre, not total turns<\/strong>. Spread 1,000 turns over a metre and you get a tenth of what you get packing them into 10 cm.<\/p>\n\n<p>Once you have <em>n<\/em> and <em>I<\/em>, the arithmetic is quick by hand \u2014 or you can run the numbers straight through our <a href=\"https:\/\/physicsfundamentalsinfo.com\/calculators\/magnetic-field\">Magnetic Field Calculator<\/a>, which solves B = \u03bc<sub>0<\/sub>nI in either direction and shows the working line by line.<\/p>\n\n<h3>A Note on \u03bc<sub>0<\/sub> That Most Textbooks Skip<\/h3>\n\n<p>For decades \u03bc<sub>0<\/sub> was <em>exactly<\/em> 4\u03c0 \u00d7 10<sup>\u22127<\/sup>, because the old definition of the ampere made it so by decree. Since the 2019 revision of the SI, it is a measured quantity instead.<\/p>\n\n<p>The <a href=\"https:\/\/physics.nist.gov\/cuu\/Constants\/index.html\" target=\"_blank\" rel=\"noopener\">CODATA 2022 value from NIST<\/a> is 1.25663706127 \u00d7 10<sup>\u22126<\/sup> N\/A<sup>2<\/sup>, which differs from 4\u03c0 \u00d7 10<sup>\u22127<\/sup> by roughly one part in ten billion. Keep using 4\u03c0 \u00d7 10<sup>\u22127<\/sup> \u2014 your calculator, your textbook and your examiner all still do.<\/p>\n\n<h2>How Does an Electromagnet Actually Work?<\/h2>\n\n<p>An electromagnet works because moving charge creates a magnetic field, and a coil arranges many such fields so they reinforce each other down its axis. Here is the chain, step by step.<\/p>\n\n<ol>\n<li><strong>Current flows.<\/strong> Connect the coil to a supply and charge moves through the wire. The size of that current is set by <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/ohms-law\/\">Ohm&#8217;s law<\/a>: I = V\/R, where R is the resistance of the whole length of wire you wound.<\/li>\n<li><strong>Each turn makes a loop of field.<\/strong> A single current loop produces a field that threads through its centre, like a very weak bar magnet.<\/li>\n<li><strong>The turns add up.<\/strong> Stack the loops side by side and their fields line up head to tail, producing a strong, near-uniform field down the middle and near-cancellation outside.<\/li>\n<li><strong>The core amplifies.<\/strong> Iron is full of microscopic magnetic domains pointing in random directions. The coil&#8217;s field swings them into alignment, and the aligned iron then contributes a field of its own \u2014 usually far larger than the coil&#8217;s.<\/li>\n<\/ol>\n\n<figure class=\"pf-figure\" style=\"margin:1.6em 0;\"><img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/electromagnet-two-panels-comparing-magnetic-domains.webp\" width=\"1440\" height=\"640\" alt=\"Electromagnet - Two panels comparing magnetic domains inside an iron core: randomly oriented with the current off, and aligned with the current on\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;max-width:720px;display:block;margin:0 auto;\" \/><\/figure>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;margin-top:4px;\">Inside a soft-iron core, the coil&#8217;s field acts as a conductor&#8217;s baton \u2014 the domains fall into step, and their combined field dwarfs the coil&#8217;s own.<\/p>\n\n<p>Soft iron is chosen precisely because it is bad at holding a grudge. When the current stops, the domains scramble again and the magnetism collapses. Hardened steel would keep much of it \u2014 useful for making permanent magnets, useless for a crane.<\/p>\n\n<div class=\"pf-sim-slot\"><div class=\"pf-sim-slot-header\"><span class=\"icon-dot\"><\/span><span class=\"label\">Electromagnet 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\/electromagnet.html?embed=1\" class=\"pf-sim-frame\" loading=\"lazy\"><\/iframe><\/div><\/div>\n\n<h2>How Do You Make an Electromagnet Stronger?<\/h2>\n\n<p>There are exactly three levers in B = \u03bc<sub>r<\/sub>\u03bc<sub>0<\/sub>nI, and they are wildly unequal in power. Ranked by how much bang they give you:<\/p>\n\n<h3>1. Add a Ferromagnetic Core (Worth Hundreds of Times)<\/h3>\n\n<p>This is not a lever so much as a different machine. Slide a soft-iron rod into an air-cored coil and the field jumps by a factor of \u03bc<sub>r<\/sub> \u2014 typically in the hundreds, sometimes the thousands for specialised alloys.<\/p>\n\n<p>Be careful with \u03bc<sub>r<\/sub> values you find quoted, though. Relative permeability is <em>not<\/em> a fixed material constant: it depends on how hard the material is being driven and on its magnetic history, which is why the same iron is listed as 200 in one book and 5,000 in another.<\/p>\n\n<h3>2. Increase the Turns Density (Worth a Lot, With a Catch)<\/h3>\n\n<p>Pack more turns into the same length and <em>n<\/em> rises in direct proportion. The catch is that more wire means more resistance, and at a fixed supply voltage more resistance means less current.<\/p>\n\n<p>Those two effects can cancel exactly \u2014 Worked Problem 6 below shows a coil where doubling the turns changes the field by nothing at all. The way round it is to shorten the coil or use thicker wire, not simply to wind more.<\/p>\n\n<h3>3. Increase the Current (Worth Least, Costs Most)<\/h3>\n\n<p>Field is directly proportional to current, so doubling <em>I<\/em> doubles <em>B<\/em> \u2014 right up until it doesn&#8217;t. Two ceilings appear fast.<\/p>\n\n<ul>\n<li><strong>Heating.<\/strong> Power dissipated in the coil is I<sup>2<\/sup>R, so doubling the current quadruples the heat. This is what actually destroys most homemade electromagnets \u2014 melted enamel, then a short, then smoke.<\/li>\n<li><strong>Saturation.<\/strong> Once every domain in the core is aligned, there is nothing left to align. For iron and silicon steel that ceiling sits at roughly 2 T, and beyond it extra current buys you only warmth.<\/li>\n<\/ul>\n\n<figure class=\"pf-figure\" style=\"margin:1.6em 0;\"><img src=\"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-content\/uploads\/2026\/08\/electromagnet-magnetic-field-b-against-current.webp\" width=\"1440\" height=\"804\" alt=\"Graph of magnetic field B against current for an iron-cored electromagnet, showing a linear rise that flattens off at about 2 tesla where the core saturates\" loading=\"lazy\" decoding=\"async\" style=\"width:100%;height:auto;max-width:720px;display:block;margin:0 auto;\" \/><\/figure>\n\n<p style=\"text-align:center;font-size:13px;font-style:italic;color:#1F2E47;margin-top:4px;\">The red dashed line is B = \u03bc<sub>0<\/sub>nI taken literally. The gold curve is what a real iron core does \u2014 it tracks the prediction, then quietly gives up.<\/p>\n\n<h3>How Strong Is Strong? A Sense of Scale<\/h3>\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;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Source<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Typical field<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Notes<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Earth&#8217;s magnetic field<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">25\u201365 \u03bcT<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">The baseline a compass reads<\/td><\/tr>\n<tr style=\"background:#F5F2EA;\"><td style=\"padding:10px;border:1px solid #D9CFB8;\">Air-cored school solenoid<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">about 5 mT<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Roughly 100 times Earth&#8217;s field<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Fridge magnet (at its surface)<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">a few mT<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Permanent, not switchable<\/td><\/tr>\n<tr style=\"background:#F5F2EA;\"><td style=\"padding:10px;border:1px solid #D9CFB8;\">Same solenoid, iron core<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">about 1 T<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">The core does nearly all the work<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Loudspeaker magnet gap<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">about 1 T<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Drives the voice coil<\/td><\/tr>\n<tr style=\"background:#F5F2EA;\"><td style=\"padding:10px;border:1px solid #D9CFB8;\">Iron saturation limit<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">about 2 T<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">A hard ceiling for iron cores<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Clinical MRI scanner<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">1.5\u20133 T<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Superconducting, no iron core needed<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>Use the top row as a sanity check on any answer you calculate. Earth&#8217;s field, per <a href=\"https:\/\/www.ncei.noaa.gov\/products\/geomagnetism-frequently-asked-questions\" target=\"_blank\" rel=\"noopener\">NOAA&#8217;s geomagnetism data<\/a>, runs 25\u201365 \u03bcT \u2014 so if your homemade coil comes out at 40 T, you have dropped a factor somewhere.<\/p>\n\n<h2>Real-World Examples of Electromagnets<\/h2>\n\n<p>Electromagnets earn their keep wherever magnetism needs to be switched, reversed or precisely dialled. Five places they turn up:<\/p>\n\n<ul>\n<li><strong>Scrapyard lifting magnets.<\/strong> A crane picks up several tonnes of steel, swings it over the sorting bay, and cuts the current. The load drops instantly \u2014 something no permanent magnet could ever do.<\/li>\n<li><strong>Electric motors.<\/strong> Coils on the rotor become electromagnets whose poles flip at just the right moment, so they are perpetually chasing the stator&#8217;s poles and never catching them.<\/li>\n<li><strong>MRI scanners.<\/strong> A superconducting coil carries an enormous current with zero resistance, holding 1.5\u20133 T steady for years without a scrap of iron in the bore.<\/li>\n<li><strong>Relays and solenoid valves.<\/strong> A small coil current pulls an iron armature, which throws a much larger switch. This is how a 5 V signal from a microcontroller commands a 240 V appliance.<\/li>\n<li><strong>Loudspeakers and headphones.<\/strong> A coil sitting in a permanent magnet&#8217;s field carries the audio signal; the varying force shoves the cone back and forth thousands of times a second.<\/li>\n<\/ul>\n\n<p>In practice, one detail decides whether an electromagnet is any good: how little air is left in the magnetic path. Flux crossing an air gap loses most of the benefit of the core, which is why lifting magnets are built with a flat pole face that sits hard against the load.<\/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\/08\/DYNASET-MAG-tatti-Kuusakoski-Liebherr-2025-02-Print-scaled-1.jpg\"\n       alt=\"Scrapyard crane electromagnet lifting a load of scrap steel\"\n       loading=\"lazy\"\n       style=\"width:100%;height:auto;border-radius:4px;\" width=\"1920\" height=\"1280\">\n  <figcaption style=\"font-size:13px;color:#1F2E47;font-style:italic;margin-top:8px;\">A lifting electromagnet holds tonnes of steel \u2014 until the operator cuts the current.<\/figcaption>\n<\/figure>\n\n<h2>Electromagnet vs Permanent Magnet: What Is the Difference?<\/h2>\n\n<p>The difference is control. A permanent magnet&#8217;s field is baked in at manufacture; an electromagnet&#8217;s field is whatever you tell it to be, moment to moment.<\/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;\">\n<thead>\n<tr style=\"background:#0A1628;color:#FAF6EE;\">\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Property<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Electromagnet<\/th>\n<th style=\"padding:10px;text-align:left;border:1px solid #D9CFB8;\">Permanent magnet<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Source of field<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Electric current in a coil<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Permanently aligned domains<\/td><\/tr>\n<tr style=\"background:#F5F2EA;\"><td style=\"padding:10px;border:1px solid #D9CFB8;\">Can it be switched off?<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Yes, instantly<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">No<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Strength adjustable?<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Yes, by varying the current<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">No, fixed<\/td><\/tr>\n<tr style=\"background:#F5F2EA;\"><td style=\"padding:10px;border:1px solid #D9CFB8;\">Poles reversible?<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Yes, reverse the current<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">No, only by physically turning it<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Needs power?<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Yes, continuously<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">No<\/td><\/tr>\n<tr style=\"background:#F5F2EA;\"><td style=\"padding:10px;border:1px solid #D9CFB8;\">Fails when?<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Power cut, or coil overheats<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Overheating or a hard knock<\/td><\/tr>\n<tr><td style=\"padding:10px;border:1px solid #D9CFB8;\">Practical top field<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Tens of tesla with superconductors<\/td><td style=\"padding:10px;border:1px solid #D9CFB8;\">Roughly 1 T at the surface<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n<p>That &#8220;fails when&#8221; row is not trivia. A scrapyard magnet dropping its load on a power cut is a genuine safety design problem, which is why some lifting systems carry backup batteries and others use permanent magnets that are mechanically shunted instead.<\/p>\n\n<h2>Common Misconceptions About Electromagnets<\/h2>\n\n<h3>&#8220;An Electromagnet Needs a Magnet Inside It&#8221;<\/h3>\n\n<p>It does not. A coil of wire with nothing in the middle is already a fully functioning electromagnet \u2014 weak, but real. The iron core is an amplifier, not the source; unmagnetised iron on its own does nothing at all.<\/p>\n\n<h3>&#8220;More Turns Always Means a Stronger Field&#8221;<\/h3>\n\n<p>Only if the coil length and the current stay put. Winding extra turns onto the same former adds resistance, which drops the current at a fixed voltage, and the two effects can cancel exactly. Problem 6 below works a case where 400 turns beat 200 turns by precisely zero.<\/p>\n\n<h3>&#8220;Just Keep Turning Up the Current&#8221;<\/h3>\n\n<p>Two hard limits stop you. The core saturates near 2 T, after which extra current adds essentially nothing to B \u2014 and heating scales as I<sup>2<\/sup>R, so you hit thermal failure long before you hit anything interesting.<\/p>\n\n<h3>&#8220;Any Metal Core Will Do&#8221;<\/h3>\n\n<p>Aluminium, copper and brass cores do nothing measurable, because their relative permeability is essentially 1. You need a <em>ferromagnetic<\/em> material \u2014 iron, nickel, cobalt or their alloys. A plain iron nail beats an expensive copper rod every time.<\/p>\n\n<h2>How Electromagnets Connect to the Rest of Electromagnetism<\/h2>\n\n<p>An electromagnet is where three separate ideas meet, which is exactly why exam boards love it.<\/p>\n\n<p>Running the machine backwards gives you <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electromagnetic-induction\/\">electromagnetic induction<\/a>: instead of pushing current through a coil to make a field, you move a field near a coil to make current. The size of that induced voltage comes from <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/faradays-law-formula\/\">Faraday&#8217;s law<\/a>, and the two effects are two faces of the same physics.<\/p>\n\n<p>The field itself, once created, obeys everything in our guide to the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/magnetic-field\/\">magnetic field<\/a> \u2014 including the force F = qvB on any charge that wanders into it, which is what actually spins a motor. Upstream, the <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/electric-current\/\">electric current<\/a> you feed the coil is the one quantity in the formula you directly control.<\/p>\n\n<p>One last connection worth knowing: run an electromagnet on AC and it does not just weaken, it <em>vibrates<\/em>. The attractive force depends on B<sup>2<\/sup>, so it peaks twice per cycle \u2014 which is why mains transformers hum at double the supply frequency. Our comparison of <a href=\"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/ac-vs-dc-current\/\">AC vs DC current<\/a> covers why that matters for relay and lock design.<\/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 solenoid has 500 turns wound over a length of 0.25 m and carries a current of 2.0 A. It has an air core. Find the magnetic field inside it.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: For a long air-cored solenoid, B = \u03bc<sub>0<\/sub> n I, where n = N \/ L.<\/p>\n<p>Step 2: n = 500 \/ 0.25 m = 2000 turns\/m.<\/p>\n<p>Step 3: B = (4\u03c0 \u00d7 10<sup>\u22127<\/sup> T\u00b7m\/A)(2000 m<sup>\u22121<\/sup>)(2.0 A) = 5.03 \u00d7 10<sup>\u22123<\/sup> T.<\/p>\n<p><strong>Answer: B = 5.0 mT (2 s.f.)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 2<\/div><div class=\"pf-problem-question\">Enamelled copper wire of diameter 0.50 mm is wound in a single close-packed layer. A current of 1.5 A flows and the core is air. What is the field inside?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: In a close-packed single layer, each turn occupies one wire diameter, so n = 1 \/ d.<\/p>\n<p>Step 2: n = 1 \/ (0.50 \u00d7 10<sup>\u22123<\/sup> m) = 2000 turns\/m.<\/p>\n<p>Step 3: B = (4\u03c0 \u00d7 10<sup>\u22127<\/sup>)(2000)(1.5) = 3.77 \u00d7 10<sup>\u22123<\/sup> T.<\/p>\n<p><strong>Answer: B = 3.8 mT (2 s.f.)<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 3<\/div><div class=\"pf-problem-question\">The solenoid from Problem 1 (500 turns, 0.25 m, 2.0 A) now has a soft-iron core of relative permeability 200. Find the new field, and compare it with Earth&#039;s magnetic field of about 50 microtesla.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: With a core, B = \u03bc<sub>r<\/sub> \u03bc<sub>0<\/sub> n I, so the air-core answer is simply multiplied by \u03bc<sub>r<\/sub>.<\/p>\n<p>Step 2: B = 200 \u00d7 5.03 \u00d7 10<sup>\u22123<\/sup> T = 1.005 T.<\/p>\n<p>Step 3: Ratio = 1.005 T \/ (50 \u00d7 10<sup>\u22126<\/sup> T) = 2.0 \u00d7 10<sup>4<\/sup>.<\/p>\n<p><strong>Answer: B = 1.0 T, about 20,000 times Earth&#8217;s field<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 4<\/div><div class=\"pf-problem-question\">How many turns must a 0.30 m long air-cored solenoid have to produce 8.0 mT when carrying 3.0 A?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Rearrange B = \u03bc<sub>0<\/sub> n I for turns density: n = B \/ (\u03bc<sub>0<\/sub> I).<\/p>\n<p>Step 2: n = (8.0 \u00d7 10<sup>\u22123<\/sup> T) \/ [(4\u03c0 \u00d7 10<sup>\u22127<\/sup> T\u00b7m\/A)(3.0 A)] = 2122 turns\/m.<\/p>\n<p>Step 3: N = n L = 2122 m<sup>\u22121<\/sup> \u00d7 0.30 m = 637 turns.<\/p>\n<p><strong>Answer: N is about 6.4 \u00d7 10<sup>2<\/sup> turns<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 5<\/div><div class=\"pf-problem-question\">A relay coil of 400 turns is wound over 0.050 m on a soft-iron core with relative permeability 150. The coil has a resistance of 24 ohms and runs from a 12 V supply. Find the field in the core.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Find the current from Ohm&#8217;s law: I = V \/ R = 12 V \/ 24 \u03a9 = 0.50 A.<\/p>\n<p>Step 2: Turns density n = 400 \/ 0.050 m = 8000 turns\/m.<\/p>\n<p>Step 3: B = \u03bc<sub>r<\/sub> \u03bc<sub>0<\/sub> n I = (150)(4\u03c0 \u00d7 10<sup>\u22127<\/sup>)(8000)(0.50) = 0.754 T.<\/p>\n<p><strong>Answer: B = 0.75 T (2 s.f.)<\/strong><\/p>\n<p><em>Reality note: a real relay has an air gap in its magnetic path, so the measured field would be noticeably lower than this ideal figure.<\/em><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 6<\/div><div class=\"pf-problem-question\">A 200-turn coil on a 0.10 m former has a resistance of 4.0 ohms and runs from a 6.0 V supply with an air core. It is rewound with 400 turns of the same wire on the same former, doubling the wire length and hence the resistance. Does the field increase?<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Before. I = 6.0 \/ 4.0 = 1.5 A; n = 200 \/ 0.10 = 2000 m<sup>\u22121<\/sup>. So B = (4\u03c0 \u00d7 10<sup>\u22127<\/sup>)(2000)(1.5) = 3.77 \u00d7 10<sup>\u22123<\/sup> T.<\/p>\n<p>Step 2: After. Resistance doubles to 8.0 \u03a9, so I = 6.0 \/ 8.0 = 0.75 A; n = 400 \/ 0.10 = 4000 m<sup>\u22121<\/sup>.<\/p>\n<p>Step 3: B = (4\u03c0 \u00d7 10<sup>\u22127<\/sup>)(4000)(0.75) = 3.77 \u00d7 10<sup>\u22123<\/sup> T. Doubling n while halving I leaves the product nI unchanged.<\/p>\n<p><strong>Answer: No change \u2014 B = 3.8 mT in both cases<\/strong><\/p>\n<p><em>This assumes the same wire gauge and the same mean turn circumference; a second winding layer sits at a slightly larger radius, so a real rewind is marginally worse, not better.<\/em><\/p>\n<\/div><\/details><\/div>\n\n<div class=\"pf-problem\"><div class=\"pf-problem-num\">Problem 7<\/div><div class=\"pf-problem-question\">A coil with 8000 turns per metre carries 2.0 A around an iron core quoted as having a relative permeability of 500. Calculate the predicted field and explain why the real coil cannot deliver it.<\/div><details><summary>Show Solution<\/summary><div class=\"pf-problem-solution\">\n<p><strong>Solution:<\/strong><\/p>\n<p>Step 1: Field from the coil alone: B<sub>0<\/sub> = (4\u03c0 \u00d7 10<sup>\u22127<\/sup>)(8000)(2.0) = 2.01 \u00d7 10<sup>\u22122<\/sup> T = 20.1 mT.<\/p>\n<p>Step 2: Naive prediction with the core: B = 500 \u00d7 20.1 mT = 10.1 T.<\/p>\n<p>Step 3: Iron saturates at roughly 2 T. Once every domain is aligned the core cannot contribute more, so B levels off near 2.0 T and the effective relative permeability collapses to about 2.0 \/ 0.0201 = 100.<\/p>\n<p><strong>Answer: The formula predicts 10.1 T; the real field caps at about 2 T, with \u03bc<sub>r<\/sub> falling to roughly 100<\/strong><\/p>\n<\/div><\/details><\/div>\n\n<h2>Frequently Asked Questions<\/h2>\n\n<details class=\"pf-faq-item\"><summary>What is an electromagnet in simple words?<\/summary><div class=\"pf-faq-item-answer\">\n\nAn electromagnet is a magnet you can switch on and off with electricity. It is a coil of insulated wire, usually wrapped around an iron core, that becomes magnetic only while current flows through the wire. Cut the current and the magnetism disappears almost instantly, which is what makes it useful in cranes, motors and doorbells.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>How does an electromagnet work?<\/summary><div class=\"pf-faq-item-answer\">\n\nAn electromagnet works because every electric current creates a magnetic field around itself. Coiling the wire makes each loop&#8217;s field line up with its neighbours, producing a strong, uniform field down the middle of the coil. An iron core then aligns its own magnetic domains with that field and adds a much larger field of its own.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Why does an iron core make an electromagnet stronger?<\/summary><div class=\"pf-faq-item-answer\">\n\nAn iron core is full of microscopic magnetic domains that the coil&#8217;s field pulls into alignment. Once aligned, the iron becomes a magnet in its own right and its field adds to the coil&#8217;s. The multiplication factor is the relative permeability, which for soft iron is typically in the hundreds \u2014 so the core, not the coil, does most of the work.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the formula for the magnetic field of an electromagnet?<\/summary><div class=\"pf-faq-item-answer\">\n\nThe field inside a long solenoid is B = \u03bc<sub>0<\/sub> n I, where \u03bc<sub>0<\/sub> is the permeability of free space (4\u03c0 \u00d7 10<sup>\u22127<\/sup> T\u00b7m\/A), n is the turns per metre, and I is the current in amperes. With a ferromagnetic core, multiply by the core&#8217;s relative permeability: B = \u03bc<sub>r<\/sub> \u03bc<sub>0<\/sub> n I. Note that n = N \/ L, so coil length matters as much as turn count.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>How can I make an electromagnet stronger?<\/summary><div class=\"pf-faq-item-answer\">\n\nAdd a soft-iron core first \u2014 it is worth hundreds of times more than anything else. Then raise the turns per metre by winding tightly over a short length, and finally increase the current. Watch two limits: the core saturates near 2 T, and coil heating rises as the square of the current, so more amps eventually just melts the enamel.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>What is the difference between an electromagnet and a permanent magnet?<\/summary><div class=\"pf-faq-item-answer\">\n\nAn electromagnet is powered by current and can be switched off, adjusted or pole-reversed at will; a permanent magnet has a fixed field baked in during manufacture. Electromagnets need a continuous power supply and can reach far higher fields, while permanent magnets need no power but cannot be turned off or tuned.\n\n<\/div><\/details>\n\n<details class=\"pf-faq-item\"><summary>Do electromagnets work with AC current?<\/summary><div class=\"pf-faq-item-answer\">\n\nYes, but the field reverses direction every half cycle, so an AC electromagnet cannot hold a steady pull. Because the attractive force depends on B<sup>2<\/sup>, it peaks twice per cycle and the core vibrates at double the supply frequency \u2014 the familiar mains hum. Devices needing a constant grip, such as door locks and lifting magnets, use DC instead.\n\n<\/div><\/details>\n","protected":false},"excerpt":{"rendered":"<p>An electromagnet is a coil of wire that becomes magnetic only while current flows through it. Learn how it works, what B = mu0 n I means, and the three levers that actually control its strength.<\/p>\n","protected":false},"author":1,"featured_media":820,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-819","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\/819","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=819"}],"version-history":[{"count":5,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/819\/revisions"}],"predecessor-version":[{"id":1435,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/posts\/819\/revisions\/1435"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media\/820"}],"wp:attachment":[{"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/media?parent=819"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/categories?post=819"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/physicsfundamentalsinfo.com\/blog\/wp-json\/wp\/v2\/tags?post=819"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}