Question

A single conducting loop of wire has an area of 7.26E-2 m2 and a resistance of 117 Ω. Perpendicular to the plane of the loop is a magnetic field of strength 0.289 T. At what rate (in T/s) must this field change if the induced current in the loop is to be 0.367 A?

Answer 1

Answer:

$\frac{dB}{dt}$ = 591.45 T/s

Explanation:

i = induced current in the loop = 0.367 A

R = Resistance of the loop = 117 Ω

E = Induced voltage

Induced voltage is given as

E = i R

E = (0.367) (117)

E = 42.939 volts

$\frac{dB}{dt}$ = rate of change of magnetic field

A = area of loop = 7.26 x 10⁻² m²

Induced emf is given as

$E = A\frac{dB}{dt}$

$42.939 = (7.26\times 10^{-2})\frac{dB}{dt}$

$\frac{dB}{dt}$ = 591.45 T/s