The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of

Question

The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of a conducting, circular loop with a resistance of R=3.07?and a radius of 0.024 m. The magnetic field is directed out of the paper as shown.

(a) What is the magnitude of the average induced emf in the loop if the magnitude of the magnetic field is doubled in 0.1 s? _____ mV

(b) What is the average current around the loop when the magnitude of the magnetic field is doubled? Make sure you specify the direction of the current.

___ mA

(c) What is the power (the rate in which energy) is dissipated in the loop?

___ ?W

The figure shows a uniform, 3.0-T magnetic field that is normal to the plane of a conducting, circular loop with a resistance of R=3.07?and a radius of 0.024 m. The magnetic field is directed out of the paper as shown. (a) What is the magnitude of the average induced emf in the loop if the magnitude of the magnetic field is doubled in 0.1 s? _____ mV (b) What is the average current around the loop when the magnitude of the magnetic field is doubled? Make sure you specify the direction of the current. ___ mA (c) What is the power (the rate in which energy) is dissipated in the loop? ___ ?W

Explanation / Answer

a)

here , induced EMF = change in magnetic flux /time

EMF = pi*0.024^2 *(2*3 - 3)/.1

EMF = 0.0543 V

EMF = 54.3 mV

the induced EMF is 54.3 mV

b)

Now, Using ohm's law

induced current = 0.0543/3.07

induced current = 0.0177 A

induced current = 17.7 mA

c)

Power dissipated = V*I

Power dissipated =54.3 * 17.7 *10^-6 W

Power dissipated = 3.129 *10^-4 W = 312.9 uW

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