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

Inside the circular region at distance `r`
`El=(dphi)/(dt)=S((dB)/(dt))`
`:. E(2pir)=(pir^2).(dB)/(dt)`
`E=r/2 (dB)/(dt)`
`F=qE=(qr)/2(dB)/(dt)`
At points `a` and `b`, distance from centre is `r`
`:. F=(qr)/2 (dB)/(dt)`
At point `C` distance `r=0`
`:. F=0`
`ox` magnetic field is increasing. Hence, induced current in an imaginary loop passing through `a` and `b` should produce `o`. magnetic field. Hence induced current through an imaginary circular loop passing through a and `b` shoud be anti clockwise. Force on positive charge is in the direction of induced current. Hence, force at a is towards left and force at `b` is upwards.