Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 23, Problem 76P
(a)
To determine
The proof that graph is a circle.
(b)
To determine
The description of three dimensional surface.
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What is the capacitance of a parallel plate capacitor in vacuum?
Sol.
The basic definition for capacitance is:
Since the electric potential can also be written as
V = Ed
Where, E is the electric field contribution of the parallel plate (two plane charge):
| -ol Eo
Sigma is the surface charge density given by:
By, substitution, we get the capacitance of the parallel plate to be:
C= E0*
A thin-walled, hollow, conducting cylinder with radius rb is concentric with a solid conducting cylinder with radius ra<rb. Each has length L. The two cylinders are attached by conducting wires to the terminals of a battery that supplies potential V. A solid cylindrical shell, with inner radius ra and outer radius R<rb, made of a material with dielectric constant K, slides between the conducting cylinders, as shown in (Figure 1). By changing the insertion distance x, we can alter the capacitance seen by the battery and therefore alter the amount of charge stored in this device.
a)Determine the capacitance as a function of x.
Express your answer in terms of the variables K, L, ra, rb, R, x, and constants ϵ0, π.
b) If L = 12.0 cm, ra = 1.00 cm, rb = 4.00 cm, R = 3.00 cm, and K = 3.21, what is the capacitance when x = 0?
c) What is the capacitance when x = L?
d) What value of x results in 6.00 nC of charge on the positively charged cylinder plate when V = 1.00 kV?
SET 1
3. Define equipotential surfaces.
Chapter 23 Solutions
Physics for Scientists and Engineers
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