Question

Suppose the loop in Exercise is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of 0.3 T at the rate of 0.02 T $s^{-1}$. If the cut is joined and the loop has a resistance of 1.6 ohm , how much power is dissipated by the loop as heat? What is the source of this power?

Exercise :

[ A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm $s^{-1}$ in a direction normal to the (a) longer side, (b) shorter side of the loop? For how long does the induced voltage last in each case? ]

Answer 1

$A=8\times 2=16c{m}^2$

emf, $e=\frac{d(A\times B)}{dt}=0.32\times {10}^{-4}V$

Induced current, $i=e/R=2\times {10}^{-5}A$

Power, $P=i^{2}R=6.4\times {10}^{-10}W$