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An electric field due to a positively charged long straight wire at a distance r from it is proportional to r−1 in magnitude. Two electrons are orbiting such a long straight wire in circular orbits of radii 1 A and 2A. The ratio of their respective time periods is

(a) 1 : 1

(b) 1 : 2

(c) 2 : 1

(d) 4 : 1

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Answer is : (b) 1 : 2

Electron revolve around wire due to its electrostatic force of attraction.

So, force on electron is

F = eE = ker-1

This force is necessary centripetal force.

So,

As velocity of electron is independent of radius of paths,

⇒ v1 = v2

Now, ratio of time periods of rotation are

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