1) Another chance to prove to yourselves that you can manipulate vectors!
Charges of +10nC (10^-8C) are located at the vertices of a right triangle with sides of 3cm, 4cm, and 5cm. If the triangle is arranged so that the 4cm side is the +ve x axis and the 3 cm side the +ve y axis find the force on the charge at the origin.

2) A very long cylinder with radius 15 cm is placed along the axis of a second very long cylinder of radius 1 m. A van der Graaf generator is used to create a 400,000Volt potential difference between the grounded outside cylinder and the +ve inside cylinder.
a) Find the electric field at all radii from 15 cm to 1 m, assuming that you are a very long way from the ends of the cylinders.
b) Find the electric potential at all the same radii. (We could not do this for an isolated cylinder but there is no problem here!)

3) Two circular metal disks of radius R = 1m are placed parallel to each other separated by 1 mm of vacuum. A battery maintains a potential difference of 10V between the plates.
a) What is the electric field between the plates?
b) What can you say about the charges on the plates?

4) A point charge of 1nC is placed at the centroid of a regular tetrahedron. How much electric flux flows through each of the four identical faces of the tetrahedron?

5) We learned in class that the force on a charge q moving at velocity v in a magnetic field B is given by F = qv×B. An extension of this tells us that the force on a straight wire of directed length L carrying a current I is F = IL×B. Use this and Ampere's law to find the force/unit length between two long straight wires placed parallel and a distance d apart and each carrying a current I.
What has to be true about the directions of the two currents if the wires are to attract each other?

6) Show as clearly as you can, with math and or very clear diagrams and clear words, that a particle with mass m and charge q which is introduced into a region with a uniform magnetic field B in such a way that its initial velocity v is exactly prependicular to the B field will travel in a circle and find an equation for the radius of the circle.

7) Consider a pair of model railway tracks, parallel wires with a separation of 2 cm, placed on a horizontal table in a uniform vertical magetic field B = 0.01 Tesla (100 Gauss, field lines pointing up). The left hand end of the track is shorted with a wire and a second wire is placed loosely on top of the track. When the upper wire is dragged sideways from right to left a current starts to flow in the wire.
a) Use Faraday's law to explain why a current flows.
b) Use Lenz's law to determine the direction of current flow.
c) Use the Lorentz force law to determine whether the resulting magnetic force acts to speed up the wire or slow it down and relate your answer to Lenz's law.

8) Discuss evidence that light is a transverse rather than a longitudinal wave. Be as clear and explicit as you can. Your aim should be to convice a skeptical high school senior.