A uniform magnetic field `B = 0.5 T` exists in a circular region of radius `R = 5m`. A loop of radius `R = 5 m ` encloses the magnetic field at `t = 0` and then pulled at uniform speed `v = 2m s^(-1)` In the plane of the paper. Find the induced emf `("in" V)` in the loop at time `t = 3 s`.

Answer

8

Explanation

`O_(1)M = (vt - R) + ((2R - vt)/(2)) = (vt)/(2)`

`l = 2sqrt(r^(2) - (O_(1)M)^(2)) = 2sqrt(R^(2) - ((vt)/(2))^(2)) = sqrt(4R^(2) - v^(2)t^(2))`
so `E = Bvl = Bxsqrt(4R^(2) - v^(2)t^(2))`
given `R = 5m, v = 2m//s, t = 3s`
`E = 0.5 xx2sqrt(4 xx 25 - 4 xx 9) = 8V`