A large solid sphere with uniformly distributed positive charge with smooth narrow turned through its center.A small particle with negative charge,initially at rest far from the sphere,approaches it along the line of the tunnel, reaches its surface with a speed v, and passes through the tunnel.Its speed at the center of the sphere will

Hi

Consider the force that acts on the charge wen it is inside the tunnnel . the force is Kqr/R³ .

Therefore by integrating This force with respect to r, from R to 0, then we can calculate the work done in bringing the charge q from R to 0.

This work done is responsible for change in kinetic energy of the charge,. Hence, 1/2m(v_final²- v²)= work done, hence we can find v at the centre of the sphere.