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Question -

In a chamber, a uniform magneticfield of 6.5 G (1 G = 10–4 T) is maintained. An electron isshot into the field with a speed of 4.8 × 106 m s–1 normalto the field. Explain why the path of the electron is a circle. Determine theradius of the circular orbit. (= 1.6 × 10–19 C, me=9.1×10–31 kg)



Answer -

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 electronand magnetic field, θ = 90°

Magnetic force exerted on theelectron in the magnetic field is given as:

F = evB sinθ

This force provides centripetalforce to the moving electron. Hence, the electron starts moving in a circularpath of radius r.

Hence, centripetal force exerted onthe electron,

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

Hence, the radius of the circularorbit of the electron is 4.2 cm.

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