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 = 1.5 × 10–19 C, me = 9.1 × 10–31 kg)
Given:
Magnetic field strength, B = 6.5 G = 6.5 × 10-4T
Initial velocity of electron = 4.8 × 106 ms-1
Angle between the initial velocity of electron and magnetic field, θ = 900
Force on the electron,
Fe = e × V × B × sinθ …(1)
Where,
e = charge on electron
V = velocity of electron
B = Magnetic field strength
θ = angle between direction of velocity and magnetic field
By putting the values in equation (1), we get
⇒ Fe = 1.6 × 10-19 C × 4.8 × 106 ms-1 × 6.5 × 10-4T × sin 90
⇒ Fe = 4.99 × 10-16N
This force serves as the centripetal force, which explains the circular trajectory of the electron.
Centripetal force Fc = mv2/r …(2)
By equating equation (1) and equation (2) we get,
⇒ 
⇒ 
r = 4.2 cm.
Hence the radius of the path of electron shot into the magnetic field is 4.2 cm.