# Potential of Charged Sphere

1. Feb 24, 2007

### stylez03

1. The problem statement, all variables and given/known data
The electric field at the surface of a charged, solid, copper sphere is 4200 N/C, directed toward the center of the sphere. The sphere has a radius of 0.190 m.

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

2. Relevant equations
The potential is the same outside/insider right so that leaves:

$$V_{surfrace} = \frac {q} {4*pi*(8.85*10^{-12})*R}$$

3. The attempt at a solution

$$V_{surfrace} = \frac {4200*10^{-19}} {4*pi*(8.85*10^{-12})*0.190}$$

2. Feb 25, 2007

### Hootenanny

Staff Emeritus
Note that electric field is not the same as charge.

3. Feb 25, 2007

### stylez03

So this should involved $$\vec {E}$$ somehow right?

$$E = \frac {1} {4*pi*E_{0}} * \frac {q} {R^{2}}$$

4. Feb 25, 2007

### Hootenanny

Staff Emeritus
Yes, you need to use this to determine the charge on the surface of the sphere.

5. Feb 25, 2007

### stylez03

So the relation with Electric Field to potential would be:

$$V = q*E$$ ?

6. Feb 25, 2007

### Hootenanny

Staff Emeritus
No. Take your previous equation and use to to calculate q

7. Feb 25, 2007

### stylez03

Ohhh I see

$$Q = \frac {R^{2}E} {K}$$

8. Feb 25, 2007

### Hootenanny

Staff Emeritus
9. Feb 25, 2007

### stylez03

10. Feb 25, 2007

### stylez03

hm, I tried the following equation and it said it was wrong?

$$Q = \frac {R^{2}E} {K}$$

$$Q = \frac {(0.190)^{2} * 4200} {\frac {1} {4*pi*E_{0}}}$$

$$Q = 1.68*10^{-8}$$

11. Feb 25, 2007

### Hootenanny

Staff Emeritus
The question didn't ask you for the charge, it asked you for the potential inside the sphere...

12. Feb 25, 2007

### stylez03

So after finding charge q, I need to substitute it back into

$$V = \frac {Kq} {r}$$

13. Feb 25, 2007

### Hootenanny

Staff Emeritus
Yes.......

14. Feb 25, 2007

### stylez03

I had one final question on this problem. I just got the answer, but when I did the calculation it came out to be positive value but the online program said to check my signs, meaning it should be negative. I'm not sure what the intuition is behind the solution being negative, would you know or could you explain that quickly. Thank you again for your time and patients. Starting to understand the difference for charge/potential.

15. Feb 25, 2007

### Hootenanny

Staff Emeritus
The clue is in the question
The electric field is define such that it is directed away from positive charge and towards negative charge. Or from from points of higher potential to lower potential, therefore, if the electric field is directed towards the centre of the sphere, then the centre must be at a lower potential than the outside of the sphere. Since zero potential (i.e. V=0) is taken to be at $r=\infty$, then the potential at the centre must be negative. Does that make sense? (Apologies if it doesn't but I'm running out of coffee :grumpy:)
Its been a pleasure
Once you got your head round potential vs. field vs. potential energy you'll sail the rest of electrostatics.