Question

Suppose that you have two concentric spherical shells of radii a and b, with a<b. The innershell has a charge−Qand the outer shell has a charge Q; the charges are uniformly distributed over each shell.

a. Find the potential difference between the shells, going from the inner shell to the outershell.

b. Now suppose that the shells are nearly the same size in the sense that b=a+d where d<<a. Write the leading behaviour of the potential difference in the limit whered/a1. Express the answer in terms ofσ, the absolute value of the surface charge density on the innersphere, and d.

c. How does your answer compare with the potential difference between two infinite planes, of charge densities±σ, separated by a distance d?

Answer #1

The space between two concentric conducting spherical shells of
radii b = 1.70 cm and a = 1.00 cm is filled with
a substance of dielectric constant κ = 15.1. A potential difference
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Determine (a) the capacitance of the device,
(b) the free charge q on the inner shell,
and (c) the charge q induced along the
surface of the inner shell.

a) By using Gauss’s law, find the electric field inside, outside
and inbetween two concentric spherical metal shells, assuming that
the inner shell, of radius a, carries a charge of -Q and the outer
shell, of radius b, carries a charge of Q.
b) By making use of the result in part (a), find the energy
stored in the system made of two concentric spherical metal
shells.
c) By using the result in part (a) find the electric potential
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and the larger shell has charge q2=?9.00nC distributed
uniformly over its surface. Take the electric potential to be zero
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Part A
What is the electric potential due to the two shells at the
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A spherical capacitor is composed of two thin, concentric
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a. Derive the equation for the capacitance and use it to determine
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A capacitor is formed from two concentric spherical conducting
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1-What is the energy density at r= 11.1 cm , just outside the
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2-What is the energy density at r = 15.4 cm , just
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