Potential V and electric field E for uniform charge density on sphere

In summary, the formula for calculating the potential V on a sphere with uniform charge density is V = kQ/r, where k is the Coulomb constant, Q is the charge on the sphere, and r is the distance from the center of the sphere. The electric field E is related to the potential V by the formula E = -∇V, where ∇ is the gradient operator, and the direction of the electric field can be determined by using the right-hand rule. Both the potential V and electric field E can be calculated at any point on the sphere, but they will be different for points inside and outside the sphere. As the distance from the center of the sphere increases, both the potential V and electric field E decrease following
  • #1
emiliocavalcanti
1
0
One problem I can't solve.

A uniform charge density of p coul/m3 is in the shape of a sphere of radius R.
Find expressions for the potential V and the field E at a distance r from the center, for points inside or outside the sphere.

Can u help me?
 
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  • #2
Send in your solution first...and then we can help you out better.

What is your specific problem with this?


Cheers
Vivek
 
  • #3
Two words: Gauss's Law. This should probably be the first thing to pop into your head whenever you see spherical symmetry in a problem.
 

1. What is the formula for calculating the potential V on a sphere with uniform charge density?

The formula for calculating the potential V on a sphere with uniform charge density is V = kQ/r, where k is the Coulomb constant, Q is the charge on the sphere, and r is the distance from the center of the sphere.

2. How is the electric field E related to the potential V for a sphere with uniform charge density?

The electric field E is related to the potential V by the formula E = -∇V, where ∇ is the gradient operator. This means that the electric field is equal to the negative of the gradient of the potential.

3. How do I determine the direction of the electric field E for a sphere with uniform charge density?

The direction of the electric field E can be determined by using the right-hand rule. Place your right hand with your fingers pointing in the direction of the electric field and your palm facing the surface of the sphere. Your thumb will then point in the direction of the electric field.

4. Can the potential V and electric field E be calculated at any point on the sphere?

Yes, the potential V and electric field E can be calculated at any point on the sphere using the formulas mentioned above. However, it is important to note that for points inside the sphere, the potential and electric field will be different compared to points outside the sphere.

5. How does the potential V and electric field E change as the distance from the center of the sphere increases?

As the distance from the center of the sphere increases, both the potential V and electric field E decrease. This is because the electric field and potential follow an inverse square law, meaning that they decrease as the distance squared increases.

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