Question

In a region at a distance r from z-axis, magnetic field `vec(B) = B_(0)rt hat(k)` is present where `B_(0)` is constant and t is time. Then the magnetic of induced electric field at a distance r from z-axis is given by
A. `r/2 B_(0)`
B. `(r^(2))/2 B_(0)`
C. `(r^(2))/3 B_(0)`
D. none

Answer 1

Correct Answer - C
`oint vec(E)*dvec(l)=-(d phi)/(dt)` where `phi = int B2 pi rdr=(2pi)/(3)B_(0)tr^(3)`
`E2 pi r = -(2 pi B_(0)r^(3))/(3) implies E+(B_(0)r^(2))/(3)`.