Answer any 4 of the following. Each question carries 5 marks.

1. Using diagrams and equations explain the behavior of the electric field because of the charge distribution in an infinite line, a ring, an infinite disk, and two infinite planes. Calculate the electric field 1 m outside the parallel planes (justify your calculation using equations).

2. Derive the expressions for electric fields both inside and outside a uniform spherical charge distribution using Gauss’s law. Show the behavior of the field both inside and outside of the sphere by calculating the field using the derived equations and approximately plotting them on a diagram.

3. Draw a diagram showing the electric field lines and equipotential surfaces created by an electric dipole. Write four main characteristics of the lines and surfaces that also emphasize the relationship between the lines and surfaces. Use the equations of electric field and potential for a dipole while explaining the characteristics.

4. Derive the expression for the capacitance of a spherical capacitor using Gauss’s law. Show how the capacitance changes with the shape and size of the capacitor using diagrams. What is the capacitance of a spherical capacitor if the radii of the inner and outer shells are 1 m and 2 m, respectively?

5. Show that the energy stored by a capacitor $U=CV^2/2=Q^2/2C=QV/2$. Show each step of your derivation. If the parallel plates of a capacitor are 1 mm apart and have an area of 1 cm$^2$, what is its capacitance and how much energy can it store if 5 V is applied between its plates? Is it a realistic capacitor?