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

`\epsilon = 0.018 V`

Step-by-step 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 = -(d\phi)/(dt)`

Φ = BA cos θ

`\epsilon = -(BAd(cos \theta))/(dt)`

`\epsilon = -BA (-sin \theta)(\theta))/(dt)`

`\epsilon = BA(sin \theta)(\theta))/(dt)`

now substituting all the given values

`\epsilon = 0.2 * 0.15 (sin 90^0)* 0.6`

`\epsilon = 0.018 V`

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