# An electron is accelerated to a final velocity of 99.9% the speed

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 PhysicsAnnexe (outside room 6-320).1. The SLAC Linear Accelerator (check it out at http://www.slac.stanford.edu) accelerateselectrons and other particles in a 3.2km straight line to velocities approaching thespeed 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 theaccelerator. What potential difference would be required to accelerate the electronto this final velocity? (Just for this problem ignore relativistic effects. In practicethese need to be considered. Typically for velocities greater than 10% the speed oflight.)NOTE: The SLAC linear accelerator actually uses a travelling electromagnetic waveinside a waveguide to accelerate the electrons – the electrons ?surfing’ theelectromagnetic wave is a good analogy.b. If parallel plates of charge are used to create the potential difference what would bethe 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 ringis now positively charged (total charge Q) what is the electric potential V in the verycentre of the ring in terms of Q and R ? What is the electric field strength E at thispoint? Describe how the situation changes if exactly half the ring is removed.3. A certain arrangement of charge generates the potential V where xand y are in metres (the potential is constant in the z-direction). Derive an expressionfor the electric field and draw a sketch of the field lines and equipotentials in the x-yplane. What is the magnitude and direction (given as the angle from the x-axis) of theelectric field at the point (x y z) = (2m 0.5m 0m) ?PHYS1002 S2 2010Extra problems:(A) For the ring considered in question 2 derive an expression for the potential at any pointwithin the ring.(B) A circular disk of radius R and total charge Q has the charge distributed with surfacecharge density where c is a constant. Find an expression for the electricpotential at distance z on the axis of the disk. Your expression should include R and Qbut not c.(C) An electric dipole at the origin consists of two charges ±q spaced distance s apartalong the y-axis.a) Find an expression for the potential at an arbitrary point in the x-y plane. Youranswer 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.

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