Question

A constant magnetic field passes through a single rectangular loop whose dimensions are 0.52 m x 0.64 m. The magnetic field has a magnitude of 2.0 T and is inclined at an angle of 82° 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?
(b) If the magnetic field remains constant at its initial value of 2.0 T, what is the magnitude of the rate ΔA Δt at which the area should change so that the average emf has the same magnitude?

Answer 1

Step-by-step explanation:

Given that,

Dimensions of the rectangle is 0.52 m × 0.64 m

Magnetic field, B₁ = 2 T

Final magnetic field, B₂ = 0

Time taken, t = 0.49 s

The loop is inclined at an angle of 82° with respect to the normal to the plane of the loop.

(a) The average induced emf is given by :

`\epsilon=-(d\phi)/(dt)`

`\epsilon=-(d(BA\ cos\theta))/(dt)`

`\epsilon=-Acos\theta (B_2-B_1)/(t)`

`\epsilon=-0.52* 0.64* cos(82)* (0-2)/(0.49)`

`\epsilon=0.189\ V`

(b)
`\epsilon=-(d\phi)/(dt)`

`\epsilon=-(d(BA\ cos\theta))/(dt)`

`\epsilon=-B\ cos\theta (dA)/(dt)`

`(dA)/(dt)=(\epsilon)/(-B\ cos\theta)`

`(dA)/(dt)=(0.189)/(2* cos(82))`

`(dA)/(dt)=0.679\ m^2/s`

Hence, this is the required solution.