A charged particle passes undeflected through a region containing mutually perpendicular uniform electric and magnetic fields of magnitudes E and B respectively. When the electric field is suddenly switched off, the particle is observed to move in a circular orbit of radius R . The specific charge (ratio of charge to mass) of the particle is :

Step-by-step solution

When the particle passes undeflected through the crossed electric and magnetic fields, the electric force balances the magnetic force. qE = qvB v = E B When the electric field is switched off, the particle moves in a circular path due to the magnetic field. The necessary centripetal force is provided by the magnetic force. mv^2 R = qvB R = mv qB Substituting v = E B into the above equation: R = m qB ( E B ) = mE qB^2 Rearranging for the specific charge ( q m ) : q m = E R B^2 Answer: E R B^2