Problemset3solutions

Problemset3solutions - d If the cable was f lled with a...

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P114 PROBLEM SET 3 Spring 2007 Homework to be handed in by 1800 hours on 13 February 2007 . [1] If a conducting sphere is to be charged to a potential of 10,000 V, what is the smallest possible radius of the sphere such that the electric fi eld will not exceed the dielectric strength of air? [2] What is the dielectic constant on which the induced bound charge density is a; 80% of the free charge density on the plates of a capacitor fi lled with the dielectric? b; 20% of the free charge density? c; 98% of the free charge density? [3] A 100 kilometer long coaxial cable is built to transmit electrical power between Rochester and Bu ff alo. The coaxial cable consists of a solid copper central conductor, of radius 1 cm, and a concentric outer copper conductor of radius 2.718 cm. The gap is fi lled with air. A voltage of 100,000 volts is applied between the inner and outer conductor. a. Calculate the E fi eld inside the cable. b. Calculate the total capacitance. c. Calculate the stored energy.
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Unformatted text preview: d. If the cable was f lled with a dielectric of dielectric constant κ e = 2 . 2 , calculate the stored energy. [4] For the circuit shown, f nd a; the total equivalent capacitance between the terminals b; the charge stored on each capacitor c; the total stored energy. [5] Electric charge is distributed uniformly along a thin rod of length a , with total charge Q. Take the potential to be zero at in f nity. Find the potential at the point P a distance x to the right of the rod [6] A parallel-plate capacitor of area A and plate separation d is charged to a potential di f erence V and then is disconnected from the charging source. The plates then are pulled apart until the separation is 2 d . Find expressions in terms of A, d and V for: a; the new capacitance b; the new potential di f erence c; the new stored energy d; How much work was required to change the plate separation from d to 2 d ? 1...
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