Electrical instruments canbe damaged or destroyed if they are in a rapidly chang

Question

Electrical instruments canbe damaged or destroyed if they are in a rapidly

changing magnetic field.This might occur if an instrument were located near an

electromagnet operatingunder alternating-current conditions It is possible thatthe

electromagnet’sexternal field could produce a changing magnetic flux withinthe

instrument. If theresulting induced currents are large enough, they could damagethe

instrument. Consider alaptop computer’s speaker that is near such anelectromagnet

field of1.00 ×103Twhich reverses direction every1/120 s. Assume thatthe speaker’s

coil consists of 100circular wire loops (each with radius of 3.00 cm) with atotal

resistance of1.00. According to themanufacturer of the speaker, the current in the

coil should never exceed25.0 mA.

a.) Calculate themagnitude of the average induced emf in the coil during the1/120 s interval.

b.) Does the average induced currentexceed the manufacturer’s limit?

Explanation / Answer

a) We know the formula for calculating the value of the averageinduced emf is             = (d/dt)(NBA)               = NA(dB / dt)               = N(r2)(dB / dt)               =(100)()(3.0*10-2m)2{[(1.0*10-3T)-(-1.0*10-3T)]/ (1/120s)}               =(100)()(3.0*10-2m)2{2(1.0*10-3T)(120/s)} Do the calculation work.

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