Question

A single loop of wire with an area of 0.0920 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.240 T/s.
a. What emf is induced in this loop?
b. If the loop has a resistance of 0.600Ω, find the current induced in the loop.

Answer 1

Answer:

Induced emf in the loop is 0.02208 volt.

Induced current in the loop is 0.0368 A.

Explanation:

Given that,

Area of the single loop, $A=0.092\ m^2$

The initial value of uniform magnetic field, B = 3.8 T

The magnetic field is decreasing at a constant rate, $\dfrac{dB}{dt}=0.24\ T/s$

(a) The induced emf in the loop is given by the rate of change of magnetic flux.

$\epsilon=\dfrac{-d\phi}{dt}\\\\\epsilon=A\times \dfrac{dB}{dt}\\\\\epsilon=0.092\times 0.24\\\\\epsilon=0.02208\ V$

(b) Resistance of the loop is 0.6 ohms. Let I is the current induced in the loop. Using Ohm's law :

$\epsilon=IR\\\\I=\dfrac{\epsilon}{R}\\\\I=\dfrac{0.02208}{0.6}\\\\I=0.0368\ A$

Hence, this is the required solution.