Question

In a chamber, a uniform magnetic field of 6.5 G (1 G = 10^–4 T) is maintained. An electron is shot into the field with a speed of 4.8 × 10⁶ m s^–1 normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e =1.6 × 10^–19 C, m_e= 9.1×10^–31 kg)

Answer 1

Magnetic field strength, B = 6.5 G = 6.5 × 10^–4 T
Speed of the electron, v = 4.8 × 10⁶ m/s
Charge on the electron, e = 1.6 × 10^–19 C
Mass of the electron, me = 9.1 × 10^–31 kg
Angle between the shot electron and magnetic field, θ = 90° Magnetic force exerted on the electron in the magnetic field is given as:

This force provides centripetal force to the moving electron. Hence, the electron starts moving in a circular path of radius r. Hence, centripetal force exerted on the electron,

In equilibrium, the centripetal force exerted on the electron is equal to the magnetic force i.e.,