# Electric potential related to electric field question

• David0709
In summary, the conversation discusses a non-conducting sphere with non-homogeneous charge density and the calculation of electric field and potential both inside and outside of the sphere. The electric field is found to be r^2 / 4ε0 inside the sphere and R^4 / 4ε0r^2 outside the sphere. The electric potential is calculated using the formula E=−∇V and results in R^4 /4ε0 r outside the sphere and -r^3 /12ε0 inside the sphere. However, it is noted that potential is always relative to an arbitrary zero and when R = r, the two equations for potential do not agree.
David0709

## Homework Statement

(i) Consider a non-conducting sphere of radius R with non-homogeneous charge density ρ = ρ(r) = r, where r is the radial co-ordinate.

1. (a) Find the electric field inside and outside of the sphere
2. (b) Find and plot the electric potential inside and outside of the sphere

[/B]
E=−∇V
E = KQ1Q2/r^2
V = KQ1Q2/R

## The Attempt at a Solution

For part a) Field inside the sphere = r^2 / 4ε0
Outside the sphere R^4 / 4ε0r^2

With regards to part b)
I am aware that E=−∇V

So applying this formula we have:
Outside sphere:
R^4 /4ε0 r
Inside sphere potential
-r^3 /12ε0

However when we let R = r we see these two equations for potential do not agree suggesting something (am not sure what ) is wrong.

Any help would be appreciated

David0709 said:
these two equations for potential do not agree
Potential is always relative to some arbitrary zero, often taken as the potential at infinity.
To put it another way, going from field to potential is an integration, and an integral has a constant of integration, resolved by the bounds. The result of that is just the difference in potential between the endpoints, not an absolute potential.

Last edited:

## 1. What is electric potential?

Electric potential is a measure of the potential energy an electric charge has due to its position in an electric field. It is often referred to as voltage and is measured in volts (V).

## 2. How is electric potential related to electric field?

Electric potential is closely related to electric field. The electric field is a measure of the force an electric charge experiences at a certain point, while electric potential is a measure of the potential energy the charge has at that same point. The electric potential at a point in an electric field is equal to the electric field strength multiplied by the distance from the point to the reference point.

## 3. What is the formula for electric potential?

The formula for electric potential is V = kQ/r, where V is the electric potential, k is the Coulomb's constant (9x10^9 Nm^2/C^2), Q is the charge, and r is the distance from the charge to the reference point.

## 4. How is electric potential measured?

Electric potential can be measured using a voltmeter. The voltmeter is connected to two points in an electric field, and the difference in potential between those two points is measured.

## 5. How does electric potential affect electric charges?

Electric potential affects electric charges by determining the direction and magnitude of the force they experience in an electric field. Charges will move from areas of high potential to areas of low potential, following the direction of the electric field lines.

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