{"id":701,"date":"2026-08-04T21:29:37","date_gmt":"2026-08-04T21:29:37","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=701"},"modified":"2026-08-04T21:29:38","modified_gmt":"2026-08-04T21:29:38","slug":"faradays-law-formula","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/electromagnetism\/faradays-law-formula\/","title":{"rendered":"Faraday’s Law Formula: Calculating Induced EMF"},"content":{"rendered":"\n
Definition<\/div>

\n\nThe Faraday’s law formula states that the EMF induced in a coil equals the number of turns multiplied by the rate at which magnetic flux through it changes: \u03b5 = -N(\u0394\u03a6\/\u0394t). EMF is measured in volts, flux in webers and time in seconds. The minus sign gives direction only, not size.\n\n<\/p><\/div>\n\n

Wave a magnet through a coil of wire and a voltmeter twitches. Wave the same magnet through twice as fast and the needle jumps roughly twice as far \u2014 the magnet is no stronger, only quicker. That single observation is why the equation contains a rate of change<\/em> rather than a field strength.<\/p>\n\n

The trouble starts when you have to put numbers in. Plenty of students who can explain electromagnetic induction<\/a> perfectly still drop marks by feeding the equation B when it wants \u0394B, or by quietly forgetting the coil’s 350 turns. This page is about the arithmetic \u2014 what to substitute, how to rearrange, and how to spot a nonsense answer.<\/p>\n\n

What Is the Faraday’s Law Formula?<\/h2>\n\n

The Faraday’s law formula is \u03b5 = -N(\u0394\u03a6\/\u0394t): the induced EMF equals the number of turns times the rate of change of magnetic flux through the coil. Everything else in this article is that one line, rearranged.<\/p>\n\n

\u03b5 = -N(\u0394\u03a6\/\u0394t)<\/div>\n\n

Notice what the equation does not<\/strong> contain. There is no B on its own and no \u03a6 on its own \u2014 only a change<\/em> in flux divided by the time it took. A coil parked in the strongest magnet you own produces exactly zero volts, because nothing is changing.<\/p>\n\n

Almost every calculation therefore has two stages. First work out the magnetic flux, then work out how fast it changed.<\/p>\n\n

\u03a6 = B \u00b7 A \u00b7 cos \u03b8<\/div>\n\n

Substituting the flux into Faraday’s law gives the working form you will actually use most often. When only the field strength changes and the coil faces the field square-on, cos \u03b8 = 1 and the area is fixed:<\/p>\n\n

\u03b5 = -N \u00b7 A \u00b7 (\u0394B\/\u0394t)<\/div>\n\n

This is the version that solves the majority of exam questions. The other versions come from letting A change instead of B, or letting \u03b8 change instead of either.<\/p>\n\n

Every Symbol in the Faraday’s Law Formula (and Its SI Unit)<\/h2>\n\n

Each symbol in the Faraday’s law formula has one SI unit, and mixing them up is the single biggest source of wrong answers. Learn the table below and half the marks look after themselves.<\/p>\n\n

\n\n\n\n\n\n\n\n\n\n\n\n\n
Symbol<\/th>\nQuantity<\/th>\nSI unit<\/th>\nWatch out for<\/th>\n<\/tr>\n<\/thead>\n
\u03b5<\/strong><\/td>\nInduced EMF<\/td>\nvolt (V)<\/td>\nAnswers in mV are common for small coils.<\/td>\n<\/tr>\n
N<\/strong><\/td>\nNumber of turns<\/td>\nnone (a pure count)<\/td>\nEasy to forget entirely. N multiplies your answer.<\/td>\n<\/tr>\n
\u03a6<\/strong><\/td>\nMagnetic flux through one<\/em> turn<\/td>\nweber (Wb)<\/td>\n1 Wb = 1 T\u00b7m2<\/sup> = 1 V\u00b7s.<\/td>\n<\/tr>\n
\u0394\u03a6<\/strong><\/td>\nChange in flux (final minus initial)<\/td>\nweber (Wb)<\/td>\nA decrease is negative. Keep the sign until the end.<\/td>\n<\/tr>\n
\u0394t<\/strong><\/td>\nTime over which the change happened<\/td>\nsecond (s)<\/td>\nNot the total experiment time. Convert ms to s.<\/td>\n<\/tr>\n
B<\/strong><\/td>\nMagnetic flux density<\/td>\ntesla (T)<\/td>\nConvert mT and gauss before substituting.<\/td>\n<\/tr>\n
A<\/strong><\/td>\nArea of one turn<\/td>\nsquare metre (m2<\/sup>)<\/td>\n1 cm2<\/sup> = 10-4<\/sup> m2<\/sup>, not 10-2<\/sup>.<\/td>\n<\/tr>\n
\u03b8<\/strong><\/td>\nAngle between the field and the coil’s normal<\/td>\ndegrees or radians<\/td>\nMeasured from the normal, not<\/em> from the coil’s face.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

One term deserves its own name. The product N\u03a6 is called the flux linkage<\/strong>, measured in webers (or weber-turns), and Faraday’s law can be read as “EMF equals the rate of change of flux linkage”.<\/p>\n\n

That reading is worth adopting, because it stops N drifting out of your working. If you calculate the flux linkage before and after, the N is baked in from the start.<\/p>\n\n\n<\/rect>\nReading the Faraday’s law formula<\/text>\n\u03b5<\/text>\n=<\/text>\n–<\/text>\nN<\/text>\n\u0394\u03a6<\/text>\n<\/line>\n\u0394t<\/text>\n<\/line>\ninduced EMF<\/text>\nvolts (V)<\/text>\n<\/line>\ndirection only<\/text>\n(never changes the size)<\/text>\n<\/line>\nturns<\/text>\nno unit<\/text>\n<\/line>\nchange in flux<\/text>\nwebers (Wb)<\/text>\n<\/line>\ntime for that change<\/text>\nseconds (s)<\/text>\n<\/svg>\n\n

Every symbol in the Faraday’s law formula, with the SI unit it must be substituted in.<\/p>\n\n

How to Calculate Induced EMF in Four Steps<\/h2>\n\n

To calculate induced EMF, find the flux before and after, subtract to get \u0394\u03a6, divide by the time interval, then multiply by the number of turns. The four steps below work for every standard induced-EMF question.<\/p>\n\n

    \n
  1. Find the flux at the start and at the end.<\/strong> Use \u03a6 = B\u00b7A\u00b7cos \u03b8 for each moment. Convert cm2<\/sup> to m2<\/sup> and mT to T now<\/em>, before anything else.<\/li>\n
  2. Subtract to get \u0394\u03a6.<\/strong> Always final minus initial. If the flux fell, \u0394\u03a6 is negative \u2014 that is information, not an error.<\/li>\n
  3. Divide by \u0394t, then multiply by N.<\/strong> This gives \u03b5 = -N(\u0394\u03a6\/\u0394t). Only the time during which the flux was actually changing counts.<\/li>\n
  4. Sanity-check the size and the sign.<\/strong> Quote the magnitude unless the question asks for direction.<\/li>\n<\/ol>\n\n

    That last step is the one most people skip, and it is the cheapest mark on the page. A rough feel for typical magnitudes catches a slipped power of ten instantly:<\/p>\n\n