There exists a uniform and constant magnetic field of strength `B` in the space betweent he plates of a charged parallel plate capacitor. The charge density on the plate is `sigma` and length of the plate is `l`. An electron is projected in the space between the plates along the length of the plate. It is foudn that velcoity of the electron does not change. Find the time taken by the electron to come out of the capacitor. The figure describes the situtation. Ignore the gravity.

Answer

Net Torque `=(mu_(0)i i_(0)(b-a)sin alpha)/(pi)`

Explanation

`B=(mu_(0)i_(0))/(2pir)`
`dF=(dvec(r)xxvec(B))=i drB(ox"inside")`
Due to QR and SP
Torque about point O ( perpendicular distance )
`=r sin alpha,d tau_(0)=(r sin alpha)dF=`
`rsin alpha i d B=r i dr sin alpha(mu_(0)i_(0))/(2pir),tau_(0)=(mu_(0)ii_(0))/(2pi)sin alphaint_(a)^(b)dr,`
`tau_(0)=(mu_(0)ii_(0)sin alpha(b-a))/(2pi)`
Net Torque
`=2[(mu_(0)ii_(0)(b-a)sin alpha)/(2pi)]=(mu_(0)ii_(0)(b-a)sin alpha)/(pi)`