Electric Field & Potential Inside a Charged Sphere

[Rashid101]

The electric field inside a hollow, uniformly charged sphere is zero. Does this imply that the potential is zero inside the sphere? Explain.

 

[MATLABdude]

The electric field inside a hollow, uniformly charged sphere is zero. Does this imply that the potential is zero inside the sphere? Explain.

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As a hint, what is the electric field (inside the shell, and outside), and what is the potential at infinity? With these in mind, how might you approach the potential?

 

[nlightner]

Yes, the fact that the electric field is zero inside a hollow, uniformly charged sphere does imply that the potential is also zero inside the sphere. This is because the electric field and potential are directly related and can be mathematically described by the equation E = -∇V, where E is the electric field, V is the potential, and ∇ is the gradient operator. This equation shows that when the electric field is zero, the potential must also be zero.

In the case of a hollow, uniformly charged sphere, the electric field is zero inside the sphere because the electric charges on the surface of the sphere are uniformly distributed and cancel each other out. This means that there are no electric field lines pointing inwards towards the center of the sphere, resulting in a net electric field of zero inside the sphere.

Since the electric field is zero inside the sphere, the potential must also be zero according to the equation E = -∇V. This means that there is no change in electric potential as one moves inside the sphere, and therefore the potential is constant and equal to zero throughout the interior of the sphere.

In summary, the fact that the electric field is zero inside a hollow, uniformly charged sphere implies that the potential is also zero inside the sphere due to the mathematical relationship between the two quantities.