Question

A uniform magnetic field vector B is established perpendicular to the plane of a loop of radius 2 cm, resistance 0.8 , and negligible self-inductance. The magnitude of vector B is increasing at a rate of 40 mT/s. Find the following values.
(a) the induced emf in the loop _______mV.
(b) the induced current in the loop________ mA.
(c) the rate of Joule heating in the loop_________ µW.

Answer 1

Answer

the expression of induced  emf

$e = \dfrac{d}{dt}(nAB cos\theta)$

θ is the angle between the plane and magnetic force

$e = nA cos\theta\dfrac{d}{dt}(B )$

θ = 0°

a)$e = nA cos 0^0\dfrac{d}{dt}(B )$

$e = nA \dfrac{dB}{dt}$

$e = 1 \times \pi \0.02^2 \times 40 \times 10^{-3}$

$e = 1 \times \pi \0.02^2 \times 40 \times 10^{-3}$

e = 0.05 mV

b)  induced current

 $i = \dfrac{e}{R}$

 $i = \dfrac{0.05\times 10^{-3}}{0.8}$

i = 0.063 mA

c) Rate of heat change

P = I² R

P = 0.063² x 0.8

P = 0.003175 µW