Question

A large solid sphere with uniformly distributed positive charge has a smooth narrow tunnel through its centre.

Answer 1

Answer:

Potential at infinity =V∞=0

Potential at the surface of the sphere, Vs=k=RQ

Potential at the centre of the sphere, Vc=23kRQ

Let m and −q be the mass and the charge of the particle respectively.

Let v0= speed of the particle at the centre of the sphere.

21mv2=−q[V∞−Vs]=qkRQ....(i)

21mv02=−q[V∞−Vc]=q.23kRQ....(ii)

Dividing eqn. (ii) by eqn. (i),

v2v02=23=1.5 or v0=1.5v.