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Unformatted text preview: PHY6938 Proﬁciency Exam Fall 2002 September 13, 2002 E&M
1. A positive charge is uniformly distributed throughout a very long cylindrical volume of radius R. The charge per unit volume is ρ. (a) Find the electric ﬁeld E everywhere as a function of the distance r from the axis of the cylinder. (b) Find the electric potential V everywhere as a function of r . Deﬁne V = 0 at the surface of the cylinder. (c) Sketch E and V as function of r , from r = 0 to r = 3R, showing the values of each at r = 0, R, and 3R. 2. Two small spheres of mass m are suspended from a common point by threads of length L. When each sphere carries a charge q , each thread makes an angle θ with the vertical as shown in the ﬁgure. Find an expression for the charge q at equilibrium in terms of L, m, g, θ and the Coulomb constant k . θ L θ L m q m q 3. A proton traveling with a velocity of v = 1 × 104 m/s ˆ + 2 × 104 m/s ˆ is i j located at x = 3m, y = 4m at some time t. Find the magnetic ﬁeld at time t at the following positions: (a) x = 2m,y = 2m (a) x = 6m,y = 4m (a) x = 3m,y = 6m ...
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This note was uploaded on 03/11/2012 for the course PHY 3900 taught by Professor Staff during the Fall '1 term at FSU.
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