At a distance from a uniformly charged long wire, a charged particle is thrown radially outward with a velocity u in the direction perpendicular to the wire. When the particle reaches a distance 2 from the wire its speed is found to be 2 u . The magnitude of the velocity, when it is a distance 4 away from the wire, is (ignore gravity)

Step-by-step solution

energy conservation at A & B array l qV _ + 1 2 mu ²= qV _ B + 1 2 ~m 2 u ² q [ V _ A - V _ B ]= 1 2 mu ² q 2 ₀ 2= 1 2 mu ² array energy conservation at A & C array l qV _ A + 1 2 mu ²= q V _ C + 1 2 mv ² q [ V _ A - V _ C ]+ 1 2 mu ²= 1 2 mv ² q 2 ₀ 4+ 1 2 mu ²= 1 2 mv ² 2 q 2 ₀ 2+ 1 2 mu ²= 1 2 mv ² mu ²+ 1 2 mu ²= 1 2 mv ² 3 2 u ²= 1 2 v ² v = 3 u array