An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a current I . The electron gun shoots an electron along the radius of the solenoid with speed v . If the electron does not hit the surface of the solenoid, maximum possible value of v is (all symbols have their standard meaning):

Step-by-step solution

Magnetic Field Inside Solenoid is B = μ 0 n I Velocity ν has given to the electron So, Magnetic Force F = q ν B as ν   and B are perpendicular. In a magnetic field, charge will move on a circular path. Here, If radius is just less than or equal to radius of solenoid then the electron does not hit the surface. F = q ν B = m ν 2 R ⇒ m ν = q B R a s     q = e ν = e B R m S o , V = e μ 0 n I R m