The magnetic field `B` at all points within `a` circular region of the radius `R` is uniform space and directed into the plane of the page in figure. If the magnetic field is increasing at a rate `dB//dt` what are the magnitude and direction of the force on as stationary positive point charge `q` located at points `a,b, c`? (Point a is a distance `r` above the centre of the region, point `b` is a distance `r` to the right to the centre and point `c` is at the centre of the region).

Explanation

Since the field is increasing in inward direction, so electric field will be in anticlockwise direction. So, force on a nd b are as shows in Fig. `S4.1`.
`E2 pi r = pir^(2) (dB)/(dt) rArr E = (r )/(2) (dB)/(dt)`

So force on `a` and `b`: `F = qE = (qr)/(2) (dB)/(dt)`
At centre, electric field will be zero, so no force on charge at `c`.