A particle of mass m and positive charge q, moving with a uniform velocity v, enters a magnetic field B as shown in Find The radius of the circular are it describes in the magnetic field. (b) find the angle subtended by the arc at the centre. (c ) How long does the particule stay inside the magnetic field? (d) Solve the three parts of the above problem if the charge q on the particle is negative.

Explanation

Since magnetic field is large, the particle will emerge from the same side. Since `v_|_^(ar) B`, particle will move on circular path.

`R = (mv)/(Bq)`
Angle subtended by circular arc in magnetic field at centre of circle is `pi - 2 theta`
Time to cross magnetic field
`t = (m(pi - 2 theta))/(Bq)`
Note: if a particle enters and emerges from same side, the angle of entrance `=` angle of exit.
If `q` is `-ve`

`R = (mv)/(Bq)`
Angle at centre `= 2pi - (pi - 2theta) = pi + 2 theta`
`t = (m(pi + 2 theta))/(Bq)`