# Electric potential for a sphere of charge

1. Jul 10, 2009

### peaceandlove

1. The problem statement, all variables and given/known data
A sphere with radius 65 cm has its center at the origin. Equal charges of 2 µC are placed at 72 degree intervals along the equator of the sphere. The Coulomb constant is 8.99×10 N·m^2 / C^2. (a) What is the electric potential at the origin? Answer in units of kV. (b) What is the electric potential at the north pole? Answer in units of kV.

2. Relevant equations
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3. The attempt at a solution
The capacitance of an isolated sphere is C = 4*π*ε0*R = (1/K)*R where K = electric constant = 8.99*10^9 N-m²/C². C = 7.23*10^-11 F. The total charge on the sphere is 2*10^-6*(360/72) = 10*10^-6 C. It doesn't matter where the charges are, the conducting sphere will have the same potential at all points on the surface and inside the sphere. V = Q/C = 10*10^-6 / 7.23*10^-11 = 1.38*10^5 V = 138 kV.

The "north pole" would be at the "top" of the sphere, the equator being defined by the location of the charges. Of course, there is no distinction between "top" and "bottom", but it doesn't matter, since the potential is the same everywhere on the sphere. However, my answer got marked wrong for part (b), and I'm not sure why.

2. Jul 10, 2009

### turin

I don't think that the sphere is conducting. In fact, I think that you whould basically ignore the sphere, and simply consider the ring of charges. The problem is worded strangely.

3. Jul 10, 2009

### peaceandlove

Could you please explain how you would solve for (b)? Since there are 2 µC at 72 degree intervals along the equation, I tried dividing 2 µC by C, but that is wrong as well.

4. Jul 10, 2009

### diazona

Are you familiar with this equation?
$$V = \frac{1}{4\pi\epsilon_0}\sum_i\frac{q_i}{r_i}$$
If not... you have some catching up to do