Question

A loop of wire with cross-sectional area 2 m2 is inserted into a uniform magnetic field with initial strength 2 T. The field is parallel to the axis of the loop. The field begins to grow with time at a rate of 2 Teslas per hour. What is the magnitude of the induced EMF in the loop of wire

Answer 1

Answer:

The magnitude of the induced emf in the loop of wire, $e = 0.00112 V$

Explanation:

Cross Sectional Area of the loop, A = 2 m²

Magnetic Field Strength, B = 2 T

Rate of change of magnetic field strength, dB/dt = 2 T/hr

dB/dt = 2 * 1/3600

dB/dt = 0.00056 T/s

The induced emf is given by the equation: $e = \frac{d \phi}{dt}$

$\phi = BA$

Differentiating both sides with respect to t

$\frac{d \phi}{dt} = \frac{d(BA)}{dt}\\\\\frac{d \phi}{dt} = A \frac{dB}{dt}$

Since  $e = \frac{d \phi}{dt}$

$e = A \frac{dB}{dt}\\\\e = 2 * 0.00056\\\\e = 0.00112 V$