Question

A Circular loop in the plane of a paper lies in a 0.65 TT magnetic field pointing into the paper. The loop's diameter changes from 17.5 cmcm to 6.6 cmcm in 0.48 ss .
a) Determine the direction of the induced current and justify your answer.b) Determine the magnitude of the average induced emf.c) If the coil resistance is 2.5 Ω, what is the average induced current?

Answer 1

Answer:

Explanation:

magnetic filed, B = 0.65 T

initial diameter, d = 17.5 cm

final diameter, d' = 6.6 cm

time, t = 0.48 s

(a) According to Lenz's law, the direction of induced current is clockwise.

(b) Let e is the induced emf.

initial area, A = π r² = 3.14 x 0.0875 x 0.0875 = 0.024 m²

final area, A' = π r'² = 3.14 x 0.033 x 0.033 = 0.00342 m²

change in area, ΔA = A - A' = 0.024 - 0.00342 = 0.02058 m²

The magnitude of induced emf is given by

$e=\frac{d\phi }{dt}$

$e=B\frac{\Delta A }{dt}$

e = 0.65 x 0.02058 / 0.48

e = 0.028 V

(c) R = 2.5 ohm

i = e / R

i = 0.028 / 2.5

i = 0.011 A