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In summary, the field inside and outside of a sphere of charge depends on the distance from the center, but is undefined at the surface.

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[tex]\vec{\nabla}\cdot \vec{E} = \frac{\rho}{\epsilon_0}[/tex]

or

[tex]\int \vec{E}\cdot d\vec{a} = \frac{Q_{int}}{\epsilon_0}[/tex]

in integral form.

When we solve it for a charged sphere though, it turns out that E is of a different form inside and outside and is undefined directly at the surface.

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There is just one equation. However, because the gradient is discontinuous across the surface, when we write the equation as an analytic function, it must be split into two regimes. If this bothers you, realize that if you were to try to find a single continuous function to describe the density rho both inside and outside the sphere, you would end up with the same problem: no way to do it.cefarix said:

The formula for the electric field inside a charged sphere is E = kQr/r^3, where E is the electric field, k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere.

The electric field inside a charged sphere varies inversely with the distance from the center. This means that as the distance from the center increases, the electric field decreases.

The electric field inside a charged sphere is constant and directed towards the center, while the electric field outside the sphere follows the inverse square law and is directed away from the center.

No, the electric field inside a charged sphere cannot be negative. This is because the electric field is determined by the charge of the sphere, which is always positive.

The electric field inside a charged sphere is constant and directed towards the center, while the electric field of a point charge varies with distance and is directed away from the charge. Additionally, the electric field inside a charged sphere is only present within the sphere, while the electric field of a point charge extends to infinity.

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