# Electric potential inside a hollow sphere with non-uniform charge

• RodolfoM
In summary, the electric potential inside a hollow sphere with non-uniform charge can be calculated using the formula V = kQ/r, where V is the electric potential, k is the Coulomb's constant, Q is the total charge inside the sphere, and r is the distance from the center of the sphere. The electric potential decreases as the distance from the center increases and can be negative if the total charge is negative or the distance is greater than the radius. A non-uniform charge distribution can affect the behavior of charged particles and the electric field strength inside the sphere. The shape of the sphere does not affect the electric potential as long as the charge distribution remains the same.

#### RodolfoM

Homework Statement
The electric potential on the surface of a hollow spherical shell of radius 𝑅 is 𝑉0 𝑐𝑜𝑠𝜃, where 𝑉0 is a constant. In this problem we use spherical coordinates with origin at the center of the shell. What is the potential inside the shell?

Answer: 𝑉(𝑟,𝜃) = 𝑟/𝑅 𝑉0 𝑐𝑜𝑠𝜃
Relevant Equations
Gauss's Law, Point charge potential.
I tried to find the charge distribution using the given potential but couldn't produce the correct result. Also, Gauss's Law doesn't help, as the electric flux is 0 but we don't have any symmetry. Can someone please shine a light on this? Thanks in advance..

expand the potential in terms of Legendre polynomials.

## 1. What is electric potential inside a hollow sphere with non-uniform charge?

The electric potential inside a hollow sphere with non-uniform charge is the measure of the work required to bring a unit positive charge from infinity to a specific point inside the sphere. It is affected by the distribution of charge within the sphere.

## 2. How is electric potential inside a hollow sphere with non-uniform charge calculated?

The electric potential inside a hollow sphere with non-uniform charge can be calculated using the equation V = kQ/r, where k is the Coulomb's constant, Q is the total charge of the sphere, and r is the distance from the center of the sphere to the specific point.

## 3. What is the relationship between electric potential and electric field inside a hollow sphere with non-uniform charge?

The electric field inside a hollow sphere with non-uniform charge is directly proportional to the electric potential. This means that as the electric potential increases, the electric field also increases.

## 4. How does the electric potential inside a hollow sphere with non-uniform charge vary with distance from the center?

The electric potential inside a hollow sphere with non-uniform charge decreases as the distance from the center of the sphere increases. This is because the electric field becomes weaker as the distance increases, resulting in a lower electric potential.

## 5. Can the electric potential inside a hollow sphere with non-uniform charge ever be negative?

Yes, the electric potential inside a hollow sphere with non-uniform charge can be negative. This occurs when the charge distribution within the sphere is not symmetrical, resulting in regions of higher and lower electric potential. In these cases, the electric potential at certain points may be negative.