Electric potential at the center of a sphere

[Yosty22]

Homework Statement

The electric field at the surface of a charged, solid, copper sphere with radius 0.19m is 2800 N/C , directed toward the center of the sphere.

What is the potential at the center of the sphere, if we take the potential to be zero infinitely far from the sphere?

Homework Equations

The Attempt at a Solution

Ok, so I got the correct answer, but missed the sign.

What I did was:

I know that the electric field is 3800 N/C at the surface, and I know the radius, so I calculated the electric flux through the sphere. I found the flux to be 1723.85 Vm. Then, I solved for Q_enc and found it to be 1.526*10^-8 C. Then, I used the equation V = 1/(4pi\epsilon_0)*∫dq/r to find that the potential is 722V.

My question:

The question states that the electric field points to the center of the sphere, implying the charge enclosed is negative. Is this why the potential is negative?

 

[ehild]

Homework Statement

The electric field at the surface of a charged, solid, copper sphere with radius 0.19m is 2800 N/C , directed toward the center of the sphere.

What is the potential at the center of the sphere, if we take the potential to be zero infinitely far from the sphere?

Homework Equations

The Attempt at a Solution

Ok, so I got the correct answer, but missed the sign.

What I did was:

I know that the electric field is 3800 N/C at the surface, and I know the radius, so I calculated the electric flux through the sphere. I found the flux to be 1723.85 Vm. Then, I solved for Q_enc and found it to be 1.526*10^-8 C. Then, I used the equation V = 1/(4pi\epsilon_0)*∫dq/r to find that the potential is 722V.

My question:

The question states that the electric field points to the center of the sphere, implying the charge enclosed is negative. Is this why the potential is negative?

Yes, the inward electric field means enclosed negative charge, which has negative potential with respect to infinity.

You calculated the potential at the surface of the metal sphere. When writing the answer, add that the potential is the same through the metal.

ehild