A point charge +Q is at the center of a spherical conducting...

A point charge $+Q$ is at the center of a spherical conducting shell of inner radius $R_{1}$ and outer radius $R_{2}$, as shown in $\underline{\text { Figure } 16-25 . \text { The charge on }}$ the inner surface of the shell is
A. $+Q$.
B. $-Q$.
C. 0 .
D. $+Q / 2$.
E. $-Q / 2 .$ SSM

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Key Concepts

Gauss's Law

Gauss’s Law relates the electric flux through a closed surface to the net charge enclosed by that surface. In problems involving symmetry, such as spherical shells, it is used to determine how charge distributions produce electric fields and, conversely, how induced charges arrange themselves to maintain zero electric field inside a conductor.

Conductor in Electrostatic Equilibrium

In a conductor at electrostatic equilibrium, the electric field within the conducting material is zero. This principle forces free charges within the conductor to redistribute themselves on its surfaces in response to any nearby charges, ensuring that the interior remains field-free.

Electrostatic Induction and Charge Distribution

When a charge is placed inside a hollow conductor, it induces a redistribution of charges such that an equal and opposite charge appears on the inner surface to cancel the electric field inside the conducting material. This induced charge is exactly opposite in magnitude to the internal charge, maintaining electrostatic equilibrium while preserving the overall neutrality of the conductor.

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