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Problem 1 In this problem, we will analyze the method used by J.J. Thomson in 1897 to measure the charge/mass ratio of the electron. A beam of electrons with charge q and mass m and velocity V vi enters a region that has a uniform electric field E Ei and a uniform magnetic field B- Bi. Thus the magnetic and electric fields are at right angles to each other and to the beam (a) Suppose that E is adjusted so that there is no deflection of the beam by the fields. What is the relation betwee E. v, and B (b) Now the electric field is turned off, and the radius of curvature R of the beam of electrons within the region is measured. In terms of E, B, and R, what is q/m? (c) Now suppose that B is 25 gaiss, and ?, 0.02c where c is the speed of light. Then, using the actual numerical values of q and m for the electron, what is R in meters, and E in volts/meter, for this experiment? How would these change if B were 1 Tesla? Problen 2 (a) Find the maguetic field at the center of a square loop of side a that carries a steady current I clockwise. b) Find the magnetic field at the center of a regular n-sided polygon of side a that carries a steady current I clockwise. (c) Show that your formula for part (b) reduces to the field at the center of a circular loop of radius R. in the limit n ? oo. Problem 3 Find the force on the rectangular wire loop with sides b and c, placed as shown a distance a away from an infinite straight wire carrying a current I to the right. The rectangular loop carries a current /2 clockwise

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