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In: Physics

1. An infinitely long non-conducting right-circular cylinder of radius a, oriented concentrically with the z-axis, carries...

1. An infinitely long non-conducting right-circular cylinder of radius a, oriented concentrically with the z-axis, carries uniform charge density ?0. It is surrounded concentrically by an infinite long grounded right-circular conducting cylindrical shell of inner radius b and outer radius c. Ground potential is zero.
(a) (4 points) What is the linear charge density (charge per unit length) ? of the inner nonconducting cylinder.
(b) (4 points) What are the linear charge densities (charge per unit length) ? on the surfaces of the conducting shell at ?=? and ?=?, where ? is the radial cylindrical coordinate measured from the z-axis?
(c) (12 points) What is the electric field in the regions ?<?,?<?<?,?<?<?, and ?>??

2. (20 points) For the configuration in Problem 1, what is the electric potential along the z-axis, i.e. at ?=0, assuming the ground potential is zero?

3. An ideal parallel plate capacitor with capacitance ?0 is charged to potential ∆?0. How much work is done in terms of ?0 and ∆?0 (the initial potential difference between the plates) in separating the plates to double their initial separation when:
(a) (10 points) the plates are charged to potential difference ∆?0 and insulated, i.e. removed from the charging battery, before being separated;
(b) (10 points) the plates are permanently connected to a battery which maintains a potential difference ∆?0 between the plates while they are being separated?
(Your answers to this problem must be expressed in terms of ?0 and ∆?0, not in terms of the charge on the plates, since that is not a given quantity.)   

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Questions involving charge densities,electric fields and electric potentials at different locations of a system consisting of charged dielectric and grounded conductor having cylindrical symmetry


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