(a) Two spheres have radii a and b, and their centersare a distance d apart. Show that the capacitance of this sys-tem is4TE,C =11+b2|adprovided d is large compared with a and b. Suggestion:Because the spheres are far apart, assume the potential ofeach equals the sum of the potentials due to each sphere.(b) Show that as d approaches infinity, the above resultreduces to that of two spherical capacitors in series.

Answered: Image /qna-images/answer/91cb1e15-554b-4bef-a486-8f579589e708.jpg

Answered: (a) Two spheres have radii a and b, and…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter7: Electric Potential

Section: Chapter Questions

Problem 60P: A metallic sphere of radius 2.0 cm is charged with +5.0C charge, which spreads on the surface of the...

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A parallel-plate capacitor with capacitance 5.0F is charged with a 12.0-V battery, after which the battery is disconnected. Determine the minimum work required to increase the separation between the plates by a factor of 3.
Check Your Understanding When a cylindrical capacitor is given a charge of 0.500 nC, a potential difference of 20.0 V is measured between the cylinders, (a) What is the capacitance of this system? (b) If the cylinders are 1.0 m long, what is the ratio of their radii?
Two very large metal plates are placed 2.0 cm apart, with a potential difference of 12 V between them. Consider one plate to be at 12 V, and the other at 0 V. (a) Sketch the equipotential surfaces for 0, 4, 8, and 12 V. (b) Next sketch in some electric field lines, and confirm that they are perpendicular to the equipotential lines.
Check Your Understanding The capacitance of a parallel-plate capacitor is 2.0 pF. If the area of each plate is 2.4 cm2, what is the plate separation?
If a proton is released from rest in an electric field, will it move in the direction of increasing or decreasing potential? Also answer this question for an electron and a neutron. Explain why.
Check Your Understanding The potential difference across a 5.0-pF capacitor is 0.40 V. (a) What is the energy stored in this capacitor? (b) The potential difference is now increased to 1.20 V. By what factor is the stored energy increased?
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Check Your Understanding The radius of the outer sphere of a spherical capacitor is five times the radius of its inner shell. What are the dimensions of this capacitor if its capacitance is 5.00 pF?
(i) Rank the following five capacitors from greatest to smallest capacitance, noting any cases of equality, (a) a 20-F capacitor with a 4-V potential difference between its plates (b) a 30-F capacitor with charges of magnitude 90 C on each plate (c) a capacitor with charges of magnitude 80 C on its plates, differing by 2 V in potential. (d) a 10-F capacitor storing energy 125 J (e) a capacitor storing energy 250 J with a 10-V potential difference (ii) Rank the same capacitors in part (i) from largest to smallest according to the potential difference between the plates, (iii) Rank the capacitors in part (i) in the order of the magnitudes of the charges on their plates, (iv) Rank the capacitors in part (i) in the order of the energy they store.
Suppose that the capacitance of a variable capacitor can be manually changed from 100 pF to 800 pF by turning a dial, connected to one set of plates by a shaft from 0° to 180°. With the dial set at 180° (corresponding to C — 800 pF), the capacitor is connected to a 500-V source. After charging, the capacitor is disconnected from the source, and the dial is turned to 0°. If friction is negligible, how much work is required to turn the dial from 180° to 0°?
How many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?
A metallic sphere of radius 2.0 cm is charged with +5.0C charge, which spreads on the surface of the sphere uniformly. The metallic sphere stands on an insulated stand and is surrounded by a larger metallic spherical shell, of inner radius 5.0 cm and outer radius 6.0 cm. Now, a charge of 5.0C is placed on the inside of the spherical shell, which spreads out uniformly on the inside surface of the shell. If potential is zero at infinity, what is the potential of (a) the spherical shell, (b) the sphere, (c) the space between the two, (d) inside the sphere, and (e) outside the shell?

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