Electrical potential inside a sphere using integration

In summary, the formula for calculating the electrical potential inside a sphere using integration is V = k * Q * (1/r - 1/R). This differs from the potential outside the sphere as it takes into account all charges within the sphere. The potential can be negative and decreases as the distance from the center of the sphere increases. The shape of the sphere does not affect the potential as long as the charge is uniformly distributed.
  • #1
PANTS187
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Homework Statement


Find the electrical potential inside a spherical shell carrying a
total charge Q by integrating over the surface.

Homework Equations


E=k q/r^2

The Attempt at a Solution


I know the answer is zero from Gauss's law, but I don't know how to do the integration to get it.
 
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  • #2
Do you want to use gauss' law or coulombs law? What integration are you asking about?
This also might be more of a math problem.
 

FAQ: Electrical potential inside a sphere using integration

What is the formula for calculating electrical potential inside a sphere using integration?

The formula for calculating the electrical potential inside a sphere using integration is V = k * Q * (1/r - 1/R), where V is the potential, k is Coulomb's constant, Q is the charge of the sphere, r is the distance from the center of the sphere, and R is the radius of the sphere.

How is the electrical potential inside a sphere using integration different from the potential outside the sphere?

The electrical potential inside a sphere using integration takes into account the contribution of all the charges within the sphere, whereas the potential outside the sphere only takes into account the charge on the surface of the sphere.

Can the electrical potential inside a sphere using integration be negative?

Yes, the electrical potential inside a sphere using integration can be negative. This can occur if the charge on the sphere is negative or if the distance from the center of the sphere is larger than the radius of the sphere.

How does the electrical potential inside a sphere using integration change as the distance from the center of the sphere increases?

As the distance from the center of the sphere increases, the electrical potential inside the sphere decreases. This is because the potential is inversely proportional to the distance from the center of the sphere.

Is the electrical potential inside a sphere using integration affected by the shape of the sphere?

No, the electrical potential inside a sphere using integration is not affected by the shape of the sphere as long as the charge is uniformly distributed within the sphere. The only factors that affect the potential are the charge and distance from the center of the sphere.

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