Problem Sheet 

• Use the Model, Visualize, Solve and Assess pattern as described in the text.
• Fill in and attach a cover sheet to the front of your solutions
• Submit your individual solutions to the three problems to the tutorial slot in the Physics

Annexe (outside room 6-320).

1. The SLAC Linear Accelerator (check it out at http://www.slac.stanford.edu) accelerates electrons and other particles in a 3.2km straight line to velocities approaching the speed of light and then smashes them together to reveal the internal makeup of matter. a. An electron is accelerated to a final velocity of 99.9% the speed of light by the accelerator. What potential difference would be required to accelerate the electron to this final velocity? (Just for this problem ignore relativistic effects. In practice these need to be considered. Typically for velocities greater than 10% the speed of light.)

NOTE: The SLAC linear accelerator actually uses a travelling electromagnetic wave inside a waveguide to accelerate the electrons - the electrons ?surfing' the electromagnetic wave is a good analogy.

b. If parallel plates of charge are used to create the potential difference, what would be the electric field strength between the plates?

2. A long copper wire of length has been shaped into a perfect ring of radius R. If the ring is now positively charged (total charge Q), what is the electric potential V in the very centre of the ring, in terms of Q and R ? What is the electric field strength E at this point? Describe how the situation changes if exactly half the ring is removed.

3. A certain arrangement of charge generates the potential V, where x and y are in metres (the potential is constant in the z-direction). Derive an expression for the electric field, and draw a sketch of the field lines and equipotentials in the x-y plane. What is the magnitude and direction (given as the angle from the x-axis) of the

electric field at the point (x,y,z) = (2m, 0.5m, 0m) ?

PHYS1002 S2 2010

Extra problems:

(A) For the ring considered in question 2, derive an expression for the potential at any point within the ring.

(B) A circular disk of radius R and total charge Q has the charge distributed with surface charge density , where c is a constant. Find an expression for the electric

potential at distance z on the axis of the disk. Your expression should include R and Q but not c.

(C) An electric dipole at the origin consists of two charges ±q spaced distance s apart along the y-axis.

a) Find an expression for the potential at an arbitrary point in the x-y plane. Your answer will be in terms of q, s, x, and y.

b) Use the binomial approximation to simplify your result when s c) Assuming, s electric field for a dipole.