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ELECTROMAGNETIC FIELD THEORY FALL 2002 NAME: _________________________________________ Problem 1: ____________________________________ (30 pts) Problem 2: ____________________________________ (20 pts) Problem 3: ____________________________________ (20 pts) Problem 4: ____________________________________ (20 pts) Problem 5: ____________________________________ (20 pts) Problem 6: ____________________________________ (10 pts) Problem 7: ____________________________________ (24 pts) Problem 8: ____________________________________ (16 pts) Total: ____________________________________ (160 pts) Grade: ____________________________________ 1. The electric potential for the wedge capacitor shown below is only a function of . Given that electric potential on the plates of the wedge capacitor is V( = 0) = 0 and V ( = ) = Vo, find the electric field between the capacitor plates. You can treat the plates as infinitely large in area and an infinitesimal insulator along the z-axis prevents the plates from shorting out the voltage supply. (Hint: Start with Laplace’s Equation) z V=0 Vo y x 1. Continued 2. A +3.0 uC and -4.0 uC charge are located 2.0 cm and 3.0 cm respectively above a grounded metal plate as shown below. What is the electric potential at point P which is 1.0 cm above the plate? (Hint: Method of Images) 3 cm 2 cm P 1 cm 3. Find the electric potential at a distance z above the center of a flat circular disk of radius R as shown below. P z R 4. An electric field is represented by E a y î a x ĵ where a = 100 volts/m2. A. Find the charge density at any point. B. Find the electric potential function V, taking V=0 at the origin. 5. A hollow spherical shell carries charge density ρ shown below. a b A. What is the electric field in the region a r b ? k in the region a r b as r2 B. What is the electric field in the region r < a? 6 6. Evaluate the integral: (3x 4 2 2x 1) δ 3x 6 dx 7. Matching Find the charge distribution that will produce the given electric field strength or electric potential. Each object is centered at the origin and any given potentials are measured with respect to zero potential at infinity. (If you have a question about this problem, please ask it!!) A. Point Charge at the Origin B. Electric Dipole at the Origin C. Charged Metal Sphere D. Charged Hollow Metal Cylinder E. Uniformly Charged Cylinder F. Electric Quadrupole at the Origin G. Charged Metal Plate H. Uniformly Charged Sphere _____ V 1 r2 r for r a _____ E 1 for r a r 2 E 0 for z 0 _____ E 0 otherwise 0 for r a _____ E 1 for a r r V0 for r a _____ V V0 a for a r r 1 _____ E 2 r 8. Prove that the vector A 3 x 2 y z î 2xz ĵ 4zx k̂ can not represent an electrostatic field.