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

step 1 The sphere, a conducting sphere, which is minus six microcolon charge, right? And then this cond

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 carries a total charge of $+1 \mu \mathrm{C}$. The conductors are in electrostatic equilibrium. Determine the charge on the outer surface of the shell. [Hint: Sketch a field line diagram.]

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 the context of conductors, this law is used to deduce that the net charge within any region of the conductor must be zero when the electric field is zero, which in turn helps determine the distribution of induced charges on surfaces.

Electrostatic Equilibrium in Conductors

In electrostatic equilibrium, the electric field inside a conductor is zero. This condition causes free charges to rearrange themselves on the surface of the conductor such that any internal Gaussian surface within the material encloses no net charge. This concept is key when analyzing how charges distribute themselves between the inner and outer surfaces of conductors.

Charge Induction and Distribution on Conductors

When a charged object is placed near or inside a conductor, it induces a charge on the nearby surface in order to cancel out the internal electric field. For a conductor with a cavity, the inner surface will acquire a charge equal in magnitude and opposite in sign to the enclosed charge, while the remaining net charge of the conductor appears on the outer surface.

Conservation of Charge

The conservation of charge principle states that the total charge in an isolated system remains constant. This is important when calculating the outer surface charge of a conductor, as the sum of the induced inner surface charge and the outer surface charge must equal the conductor’s overall net charge.

Transcript

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