A magnetic field of instantaneous induction B is confined to a cylindrical volume of radius R. B is increasing at a constant rate of 0.01 T/s. What is the instantaneous acceleration experienced by an electron placed at a distancer `(r ltR)` from the centre?

Explanation

Magnetic flux through radius r is
`phi_r` = magnetic field `xx` area
Now `(dphi_r)/(dt)=d/(dt)(Bpir^2)`
`implies (dphi_r)/(dt)=pir^2(dB)/(dt)`

Electric field at point P is E such that
`ointE.dI=(dphi)/(dt)`
`ointEdl cos 0^@=pir^2(dB)/(dt)`
`Eointdl=pir^2(dB)/(dt)`
`E 2pir=pir^2(dB^4)/(dt)`
`implies E =r/2 (dB)/(dt)`
So, force on electron = charge x electric field
`=q^(-E) ` (where, `q^(-)` is charge on electron)
Acceleration of electron
`= (q^(-)E)/(m_e)` = (where, ma is mass of electron)
`= (q^(-)r)/(m_e2)(dB)/(dt)= (q^(-)r)/(2m_e)(0.01)`
`= (1)/200(q^(-)r)/(m_e)`