THE UNIVERSITY OF BRITISH COLUMBIA
 
Physics 122 Assignment # 3:
 
ELECTRIC CHARGE
 
Wed. 16 Jan. 2002 - finish by Fri. 25 Jan.

1.

TRIANGLE of CHARGES: Derive an expression for the work required to bring four charges of equal magnitude but different signs (as shown) together into an equilateral triangle of side a with one charge at the centre of the triangle. (Initially the charges are all infinitely far apart.)

2.

LINES of CHARGE: An infinite line of charge with linear charge density $\lambda = 5 % \times 10^{-10}$ C/m lies along the x-axis (y=0, z=0 and $-\infty < x < +\infty$). A second infinite line of charge with exactly the opposite charge density lies along the z axis. What are the x, y and z components of the resultant electric field at the point (x,y,z) = (4,4,4) m?

3.

PLANE of CHARGE: A large flat non-conducting surface carries a uniform charge density $\sigma = 4.0 % \times 10^{-9}$ C/m². A small circular hole has been cut out of the middle of this sheet of charge, as shown on the diagram. Ignoring ``fringing'' of the field lines around all distant ``outside'' edges, calculate the electric field at point P a distance z = 1.0 m up from the centre of the hole along its axis. The radius of the hole is R = 0.4 m.

4.

EXTRA ELECTRONS: The Earth can be regarded as a spherical conductor from the point of view of free electrons. How many excess electrons could the Earth hold? (Assume that only electrostatic and gravitational forces are involved.)