Cathode rays of velocity 10 6 m s - 1 describe an approximate circular path of the radius 1 m in an electric field 300 V c m - 1 . If the velocity of cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be

Step-by-step solution

Cathode rays are composed of electrons, when they move in electric field a force F = e E ...(i) Acts on them, this provides the necessary centripetal force to the particles F = m v 2 r ...(ii) From Eqs. (i) and (ii), we get e E = m v 2 r ⇒ r = m v 2 e E = m 10 6 2 e ( 300 ) ...(iii) When velocity is doubled same circular path is followed, hence radius is same r = m 2 × 10 6 2 e E ...(iv) Equating Eqs. (iii) and (iv), we get m × 10 6 2 300 e = m × 2 × 10 6 2 e E ⇒ E = 300 × 4 = 1200 V c m - 1