A) Using Solid Lines Sketch Representative Lines of Force on the Diagram (3

1) Two charges of opposite sign are fixed in space forming and electric dipole, as indicated below,

(a) Using solid lines sketch representative lines of force on the diagram (3)

(b) Using dashed lines, sketch representative equipotential lines on the diagram. (2)

A small (relative to |Q|) negative charge, q0, is now placed midway between the two charges +Q and -Q (point P).

(c) Write down an expression for the magnitude of the force on q0 in terms of Q, q0 and the distance, d, between the charges +Q and -Q. What is the direction of this force ? (4)

(d) Similarly write down the expression for the magnitude of the electric field at P. (4)

(e) What is the electric potential at P (Set V = 0 at infinity) ? (4)

(f) How much work must be done to bring q0 from infinity to P ? (3)

(g) q0 is removed and the dipole is placed in a uniform electric field of 500 V/m directed to the right. Evaluate the potential energy of the dipole in this electric field, where |Q| = 3 x 108 C and the charge separation is 0.1 mm. (5)

2) A parallel plate capacitor has plates of area A, separation d/3 and is fully charged by connection to a potential difference of 2V.

(a) Obtain an expression for the charge on the plates of the capacitor in terms of A,d,V and 0. (3)

The charging battery is disconnected and the plates are pulled apart until their separation is d. Derive

expressions, in terms of A,d,V and 0, for,

(b) the new potential difference between the plates, (9)

(c) the initial (before disconnection) and final stored energy in the capacitor, and (9)

(d) the work that was necessary to separate the plates. (4)

3) The diagram shows a non conducting spherical shell having uniform (negative) charge density . Use Gauss’ law to obtain expressions for the electric field in the three regions. In each case clearly define the Gaussian surface you are using and your assumptions about the electric field.

(a) r < a (5)

(b) a < r < b (9)

(c) r > b (5)

Suppose that the shell was made from conducting material but contained exactly the same total charge.

(d) Use Gauss’ law to obtain in which region, if any, the electric field is changed and how the charge is distributed over the conducting shell. (6)

4) A plastic rod is formed into a circle of radius R. It has a positive charge +Q uniformly distributed along one-third of its circumference and a negative charge of -4Q uniformly distributed along the rest of the circumference as shown.

(a) With V = 0 at infinity, write down an expression for the electric potential (dV) at the centre of the circle due to a point charge dq on the circumference. (3)

(b) Write down the relationship between the linear charge density on the circle , dq, R and the element of angle d. (3)

(c) Obtain expressions for the linear charge densities of the positive and negative charge distributions on the circumference of the circle. (6)

(d) Using (a), (b) and (c) determine the electric potential at the centre of the circle. (8)

(e) What is the electric potential at point P on the central axis of the circle a distance z from the centre ? (5)