In class, we considered the problem of a point charge q outside a grounded, conducting sphere of radius R. Assuming that the sphere was centered at the origin, we employed the ‘method of images’ to find the electrostatic potential as V (r > R) = q − qR/a ,|⃗r − azˆ| |⃗r − (R2/a)zˆ| where a > 0 is the position of the charge q on the z-axis. Consider the analogous problem where the charge q is now placed inside a hollow, grounded, conducting sphere of inner radius R, and q is at the position a < R on the z-axis. a) Find the electrostatic potential V (r < R) inside the sphere. b) Find the induced surface-charge density σ on the sphere. c) Find the magnitude and direction of the force F⃗ acting on the charge q. d) Determine the electrostatic potential V (r < R) if the sphere is instead kept at a constant potential V0. e) Determine the electrostatic potential V (r < R) when a total charge Q is put on the sphere.
In class, we considered the problem of a point charge q outside a grounded, conducting sphere of radius R. Assuming that the sphere was centered at the origin, we employed the ‘method of images’ to find the electrostatic potential as
V (r > R) = q − qR/a ,|⃗r − azˆ| |⃗r − (R2/a)zˆ|
where a > 0 is the position of the charge q on the z-axis. Consider the analogous problem where the charge q is now placed inside a hollow, grounded, conducting sphere of inner radius R, and q is at the position a < R on the z-axis.
a) Find the electrostatic potential V (r < R) inside the sphere.
b) Find the induced surface-charge density σ on the sphere.
c) Find the magnitude and direction of the force F⃗ acting on the charge q.
d) Determine the electrostatic potential V (r < R) if the sphere is instead kept at a constant potential V0.
e) Determine the electrostatic potential V (r < R) when a total charge Q is put on the sphere.
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