Question

A coil of N turns is placed in a magnetic field `vecB` such that `vecB` is perpendicular to the plane of the coil. `vecB` changes with time as `B = B_0 cos((2 pi)/T t)` where T is time period. The magnitude of emf induced in the coil will be maximum at 

पर्याय

• `t = (nT)/8` Here, n = 1, 2, 3,  4,...

• `t = (nT)/4` Here, n = 1, 2, 3,  4,...

• `t = (nT)/2` Here, n = 1, 2, 3,  4,...

• t = nT Here, n = 1, 2, 3,  4,...

• None of the above

Answer 1

None of the above

Explanation:

Induced emf, `e = -NA * (dB)/(dt)`

`= -NA d/(dt) (B_0 cos  (2pi)/T t)`

`e = NA B_0  (2pi)/T sin  (2 pi)/T t`

For maximum magnitude of induced emf, `sin  (2pit)/T = +-1`

The value of sin will be maximum at

`pi/2, (3pi)/2, (5pi)/2, (7pi)/2`.

Therefore, `(2pi)/T t = ((2n - 1)pi)/2 or t =  ((2n - 1)T)/4`

where n = 1, 2, 3, 4,...