# 8.9 Faraday’s law of induction: lenz’s law

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• Calculate voltage, current, and magnetic fields using Faraday’s Law.
• Explain the physical results of Lenz’s Law

Faraday’s experiments showed that the voltage induced by a change in magnetic flux depends on only a few factors. First, voltage is directly proportional to the change in flux $\Delta \Phi$ . Second, voltage is greatest when the change in time $\Delta t$ is smallest—that is, voltage is inversely proportional to $\Delta t$ . Finally, if a coil has $N$ turns, a voltage will be produced that is $N$ times greater than for a single coil, so that voltage is directly proportional to $N$ . The equation for the voltage induced by a change in magnetic flux is

$V=-N\frac{\mathrm{\Delta }\mathit{\Phi }}{\mathrm{\Delta }t}.$

This relationship is known as Faraday’s law of induction    .

The minus sign in Faraday’s law of induction is very important. The minus means that the induced voltage creates a current I and magnetic field B that oppose the change in flux $\Delta \Phi$ —this is known as Lenz’s law . Faraday was aware of the direction, but Lenz stated it so clearly that he is credited for its discovery. (See [link] .)

## Applications of electromagnetic induction

Similar principles apply to computer hard drives, except at a much faster rate. Here recordings are on a coated, spinning disk. Read heads historically were made to work on the principle of induction. However, the input information is carried in digital rather than analog form – a series of 0’s or 1’s are written upon the spinning hard drive. Today, most hard drive readout devices do not work on the principle of induction, but use a technique known as giant magnetoresistance . (The discovery that weak changes in a magnetic field in a thin film of iron and chromium could bring about much larger changes in electrical resistance was one of the first large successes of nanotechnology.) Another application of induction is found on the magnetic stripe on the back of your personal credit card as used at the grocery store or the ATM machine. This works on the same principle as the audio or video tape mentioned in the last paragraph in which a head reads personal information from your card.

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