Question

A rectangular loop (area = 0.15 m2) turns in a uniform magnetic field with B = 0.20 T. At an instant when the angle between the magnetic field and the normal to the plane of the loop is p/2 rads and increasing at the rate of 0.60 rad/s, what is the magnitude of the emf induced in the loop?

Answer 1

Answer:

$\epsilon = 0.018 V$

Explanation:

given,

Area of rectangular loop = 0.15 m²

Magnetic field = B = 0.20 T

angle between magnetic field and the normal to the plane = π/2

increasing at the rate = 0.60 rad/s

magnitude of emf induced = ?

induce emf through the loop

   $\epsilon = -\dfrac{d\phi}{dt}$

      Φ = BA cos θ

   $\epsilon = -\dfrac{BAd(cos \theta)}{dt}$

   $\epsilon = -BA (-sin \theta)\dfrac{\theta)}{dt}$

   $\epsilon = BA(sin \theta)\dfrac{\theta)}{dt}$

now substituting all the given values

   $\epsilon = 0.2 \times 0.15 (sin 90^0)\times 0.6$

   $\epsilon = 0.018 V$

the magnitude of induced emf  is equal to $\epsilon = 0.018 V$