Subject: Ideal Conductors and Capacitors An infinite conducting plane has a hemispherical bump on it with radius R.  A point charge Q is located a distance R above the top of the hemisphere, as shown in the figure  below.

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Subject: Ideal Conductors and Capacitors

An infinite conducting plane has a hemispherical bump on it with radius R
A point charge Q is located a distance R above the top of the hemisphere, as shown in the figure 
below. 
a. Determine the location of the image charges needed to make the electric field 
perpendicular to the plane and the hemisphere at all points.
b. Suppose that the distance A from the given charge Q to the plane is much larger 
than the radius R of the hemisphere. Show that in this limit, the surface charge 
density at the top of the hemisphere is 3 times as large as the surface charge density 
would be on the plane if we simply had a flat plane without the hemispherical bump.

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