PHYS 220 Final, Fall 1995

PHYSICS 220 January 30, 1996, Final Exam ‘Time: 8:00 a.m. Ped iy 1. The space between two coaxial conducting cylinders of length L= 25 om is half- ; filled with a dielectric having relative dielectric constant fy = 8. The cylinders have ~ radius 0.5 cm and 2 cm, as shown (Fig. 1) and are connected to a 100 V battery. a- find the field E and 1) in the air and in the dielectric b-Find the surface charge induced on the inner conductor at points adjacent to the air, and al points adjacent to the dielectric 2. Two perfectly conducting coaxial cytinders of length I. , inner radius a, and outer. radius 6 are maintained at a potential difference V and enclose a material with Ohmic conductivity o as in fig, 2. Find the resistance of the coaxial ' cylinder configuration. : Fig. 2, 3. Calculate the force between the two current - carrying circuit fig. 3. A current I 1. flows is in circular loop carrving of radius R. An infinit wire carrying a current I, is in the plane : of the loop and at a distance d > R from the center of the loop. ( Use energy method). 4. A uniformly charged thin disk of charge density 0, radius R, and thickness t < R rotates with angular velocity 0 about the z-axis of symmetry, Calculate the B ficd at a point on the axis of the thin disk, AMERILAN PSIVENSIT LEB RARY ory ta 5. The inner sphere of a spherical capacitor (fig. 5) has a radius Ry; the outer concentric shell is very thin and has a radius R2. The inner sphere is kept at a constant potential V by a battery. The outer shell is insulated and has a charge qp. a- Calculate the potentials $y and ¢ of the inner and outer conductors. Calculate the electrostatic energy of the system. b- Suppose that the inner sphere now expands to radius R3. As a result of the expansion, the electric energy and the charge at the inner surface change. Calculate the change in electric energy. (fig. 8) . (a) show that fac = where > is magnetic flux through a surface bounded by the circuit C. . (b) Use this result together with Ampere's law to find A at distance r both inside and outside a very long solenoid. .A tong cylinder of radius a and permeability {cis placed in a uniform magnetic field Bo. " Calculate the magnetic induction inside the cylinder.[ Assume from the beginning that o* can be completely specified in terms of the cos 0 cylindrical harmonics. This assumption is justified, since all boundary conditions can be satisfied in terms of the cos 6 harmonics.