The nuclear charge (Ze) is non-uniformly distributed within a nucleus of radius R. The charge density $$\rho(r)$$ [charge per unit volume] is dependent only on the radical distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.

The electric field within the nucleus is generally observed to be linearly dependent on r. This implies

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

Positive and negative point charges of equal magnitude are kept at $$\left(0,0, \frac{a}{2}\right)$$ and $$\left(0,0, \frac{-a}{2}\right)$$, respectively. The work done by the electric field when another positive point charge is moved from $$(-a, 0,0)$$ to $$(0, a, 0)$$ is