Question

Interactive LearningWare 22.2 reviews the fundamental approach in problems such as this. A constant magnetic field passes through a single rectangular loop whose dimensions are 0.46 m x 0.68 m. The magnetic field has a magnitude of 3.0 T and is inclined at an angle of 67o with respect to the normal to the plane of the loop. (a) If the magnetic field decreases to zero in a time of 0.49 s, what is the magnitude of the average emf induced in the loop

Answer 1

Explanation:

The dimension of a single rectangular loop is 0.46 m x 0.68 m.

Magnetic field, B = 3 T

The loop is inclined at an angle of 67 degrees with respect to the normal to the plane of the loop.

It is required to find the magnitude of the average emf induced in the loop if the magnetic field decreases to zero in a time of 0.49 s.

Te induced emf in the loop is given by :

$\epsilon=\dfrac{-d\phi}{dt}\\\\\epsilon=\dfrac{-d(BA)}{dt}\\\\\epsilon=A\dfrac{dB}{dt}\cos\theta\\\\\epsilon=0.46\times 0.68\times \dfrac{3}{0.49}\times \cos(67)\\\\\epsilon=0.74\ V$

So, the magnitude of the average emf induced in the loop is 0.74 V.