The diagram shows a conducting sphere with a irregularly shaped hole in the midd

Question

The diagram shows a conducting sphere with a irregularly shaped hole in the middle. (This is a two dimensional cross-section of a three dimensional object. The hole is completely surrounded on all sides by the conductor.) nside the hole there is a charge of -6 nC. A Gaussian surface (again in 3D) is drawn so that it is entirely inside the conductor. Since E 0 inside the conducting region, the electric flux through the Gaussian surface must be fE dA 0 What is the charge on the inner surface of the conductor (i.e., the surface of the hole)? 0 -12 nC O 12 nC

Explanation / Answer

Since the charge is enclosed inside metallic sphere, there must be induced charge on the surface of the metallic portion inner side of the hole.

For net electric flux to be zero, the charge enclosed within the Gaussian surface must also be zero, since the charge already present has a magnitude of 6nc, th3 induced charge must be -6nC

Hence, the charge induced on inner portion of hole is -6nC

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