A conducting sphere that carries a total charge of +6 μC is placed at the center of a conducting

step 1 Charge on the inner surface will be given by negative 6 micropulum and since we have got net cha

A conducting sphere that carries a total charge of +6 μC is...

A conducting sphere that carries a total charge of $+6 \mu \mathrm{C}$ is placed at the center of a conducting spherical shell that also carries a total charge of $+6 \mu \mathrm{C}$. The conductors are in electrostatic equilibrium. (a) Determine the charge on the inner surface of the shell. (b) Determine the total charge on the outer surface of the shell.

Key Concepts

Gauss's Law

Gauss's Law relates the net electric flux through a closed surface to the charge enclosed within that surface. This principle is critical for solving problems with spherical symmetry, where it enables the determination of electric fields and the induced distribution of charges on surfaces of conductors.

Charge Induction in Conductors

When a charged object is placed near or within a conductor, the free electrons in the conductor redistribute themselves in response to the external electric field. This redistribution leads to induced charges that appear on the inner and outer surfaces of the conductor, ensuring that the field inside the conductor remains zero.

Charge Conservation

Charge conservation is the principle that the total electric charge in an isolated system remains constant. In the context of conductors, this means that any induced charge on one surface must be balanced by an opposite charge or by what remains on another surface, so that the overall net charge on the conductor is preserved.

Electrostatic Equilibrium

Electrostatic equilibrium in a conductor means that the electric field inside the conducting material is zero. This condition forces the free charges within the conductor to rearrange themselves, resulting in the cancellation of internal fields and the accumulation of charge solely on the conductor’s surfaces.

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