Asolid conducting sphere with radius r that carries positive charge q is concentric with a very thin insulating shell of radius 2r that also carries charge q. the charge q is distributed uniformly over the insulating shell.

The specific question is not stated, however the general idea is given in the attached picture. The electric field in each region can be found by Gauss’ Law.

at r < R:

Since the solid sphere is conducting, the total charge Q is distributed over the surface, and the electric field inside the sphere is zero.

E = 0.

at R < r < 2R:

The electric field can be found by Gauss’ Law as in the attachment. The green pencil shows this exact region.

at 2R < r:

The electric field can again be found by Gauss’ Law, the blue pencil shows the calculations for this region.

Explanation:

Gauss’ Law is straightforward when applied to spheres. The area of the sphere is , and the enclosed charge is given in the question as Q for the inner sphere, and 2Q for the whole system.

resonant frequency

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