Question

Magnetic field in a cylindrical region of radius $R$ in inward direction is as shown in figure

• A. an electron will experience no force kept at $(2R,0,0)$ if magnetic field increases with time
• B. in the above situation, electron will experience the force in negative y-axis
• C. If a proton is kept at $(0,\frac{R}{2},0)$ and magnetic field is decreasing, then it will experience the force in positive x-direction
• D. if a proton is kept at $(-R,0,0)$ and magnetic field is increasing, then it will experience force in negative y-axis

Answer 1

Answer: (B), (C), (D)

in the above situation, electron will experience the force in negative y-axis
If a proton is kept at $(0,\frac{R}{2},0)$ and magnetic field is decreasing, then it will experience the force in positive x-direction
if a proton is kept at $(-R,0,0)$ and magnetic field is increasing, then it will experience force in negative y-axis

The induced electric field will be proportional to $\frac{dB}{dt}$ and its direction will be such that it oppose this increament or decreament.

In first case, magnetic field will increase inward, hence to decrease magnetic field, electric field must induce in anticlockwise direction. Hence, electron will experience a force in -y direction.

As per above argument, in second case, to increase magnetic field, electric field must induce in clockwise direction since $\frac{dB}{dt}$ is negative. Hence, proton will experience a force in positive x direction.

In the third case, induced electric field will be anticlockwise and hence proton at given position will experience a force in negative y direction.