PHY3211: Electromagnetic theory Mid-Term examination 2002 Notes: If you accumulate more than 100 points, youtotal mark will be 100%. You do not need to evaluate any answer numerically. Remember that dx = ln x , x ∞ −∞ dx e−x = 2 √ π, dx = arctan x . 1 + x2 1. (total: 40 points) Three charges are lined up along the x-axis as follows: +q : (3, 0, 0) , −2q : (0, 0, 0) , +q : (−3, 0, 0) . (Distances are measured in meters.) a) Let S be a spherical surface centered at the origin and going through the point (0, 4, 0). What is b) Find E at (0, 4, 0). c) What is the electrostatic potential V at (0, 4, 0) (assuming V = 0 at ∞.) d) Consider the path Γ going from (0, 4, 0) to (0, −4, 0), constructed from the following three paths: first, along Γ1 : from (0, 4, 0) to (0, , 0) in the y direction, ˆ next, along Γ2 : from (0, , 0) to (0, − , 0) in a semi-circle passing on the right of the origin, last, along Γ3 : from (0, − , 0) to (0, −4, 0) in the y direction. ˆ 1 S E · dA? 2. b) (15 points) Find the magnitude of the B field at the origin. The current in the wire runs counterclockwise. carry equal currents I in opposite directions. (total: 35 points) Two infinite parallel wires. The coil is centered at the origin. and the wire is made to carry a current I going in the counterclockwise direction. 1: A coiled wire. separated by a distance d. with inner radius a and outer radius b. where r2 = x2 + y 2 . and discuss how your result agrees or disagrees with Amp`re’s law.Evaluate the work done is displacing a small test charge along Γ assuming that → 0. so that it forms a flat disk in the xy plane. Evaluate the integral C B · dl directly. a) (5 points) Find the direction of the B field in the region r < a. containing a very large uniform number N of turns per unit distance along its radius. e 3. in the xy plane. c) (15 points) Let C be a closed circular circuit of radius a/2 centered on the origin. (total: 35 points) A long string of wire is coiled. with I increasing at the rate 2 dI dt . . snakewise. such that the inner radius is a and the outer radius is b. y x FIG. as illustrated below. FIG. lies in the plane of the wires at a distance d from one of the parallel wires. a) (25 points) Find the EMF E induced in the square loop. Is the induced current clockwise or anticlockwise? Justify your answer. 2: The layout of the wires with the square frame for problem 3. b) (10 points) Assume dI/dt > 0. 3 . with sides of length d.A square loop of wire.