1. The electrostatic field E in a particular region can be expressed in terms of spherical coordinates. Derive an expression for the potential difference.

2. The electrostatic potential in a region is given by a function. Derive an expression for the electrostatic field in this region, and hence determine the field at the point x = 1.0m, y = 2.0m, z = 3.0m. Enter the numerical values for the components of this field in the boxes in the equation below:

3. A cube of volume L^3 is bounded by the planes x = 0 and x = L, y = 0 and y = L, and z = 0 and z = L. he charge density p(x) within the cube is given by and equation. Calculate the total charge contained within the cube.

4. The region between two concentric spheres of radi alpha and 3*alpha contains a uniform charge density p and elsewhere the charge density is zero. Calculate the radial component of the electric field a a distance 2a from the centre of the spheres, E(2a).