aA capacitor is formed from two hemispheres with radii a and b (a < b). Assume that these two radii are very close to each other so that the following are validapproximations.• Charge on each hemisphere is distributed uniformly over the surface of the hemisphere.• The electric field between the hemispheres is radial and its magnitude depends only on the radial coordinate r.• The electric field outside the hemispheres is negligible.Suppose that when the capacitor is charged, the charge on the inner hemisphere is Q and the charge on the outer hemisphere is –Q.(a) Let E be the radial component of the electric field between the hemispheres for a point with radial coordinate r (a

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the outer hemisphere is -Q. sordinate r (a

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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a
A capacitor is formed from two hemispheres with radii a and b (a < b). Assume that these two radii are very close to each other so that the following are valid
approximations.
• Charge on each hemisphere is distributed uniformly over the surface of the hemisphere.
• The electric field between the hemispheres is radial and its magnitude depends only on the radial coordinate r.
• The electric field outside the hemispheres is negligible.
Suppose that when the capacitor is charged, the charge on the inner hemisphere is Q and the charge on the outer hemisphere is –Q.
(a) Let E be the radial component of the electric field between the hemispheres for a point with radial coordinate r (a <r < b). Find E.
(Coding note: eg =epsilon0.)
E
(b) Find the potential difference, V = V(a) – V(b), between the hemispheres.
V
(c) Find the capacitance C of the hemispherical capacitor.

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