# Find the value of Electric potential

1. Sep 26, 2004

### ACLerok

A total electric charge of 3.10 nC is distributed uniformly over the surface of a metal sphere with a radius of 29.0 cm. The potential is zero at a point at infinity.

Find the value of the potential at 14.5 cm from the center of the sphere.

OK, i converted the nC to C and cm to m. I tried using the equation to find the potential V=k*(q/r) where q = 3.1*10^-9 C and r = .145m but the anwers i'm getting is wrong. is there anything im missing?

2. Sep 26, 2004

### Staff: Mentor

That formula for potential from a point charge applies to your problem only outside the charged sphere. Hint: What's the field inside the sphere?

3. Sep 26, 2004

### ehild

The potential is constant inside a conducting sphere. It is the same as on the surface.

ehild

4. Sep 26, 2004

### BLaH!

What do you know about the electric field inside a sphere with a uniform surface charge? The answer is the electric field is zero inside the sphere and the electric field outside the sphere is given by

$${E}(r) = \frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^2}$$

where $$Q$$ is the total surface charge on the sphere. Remember that this equation is for OUTSIDE the sphere. We can find the electric potential anywhere outside the sphere by integrating the above expression with respect to $$r$$:

$$V(r) = \int E(r) dr = \frac{Q}{4\pi\epsilon_{0}r} + C$$

Where $$C$$ is an arbitrary constant. Because $$V(\infty) = 0 \Rightarrow C = 0$$. So far it may seem like this doesn't help you too much. You need the potential at a point INSIDE the sphere. We can find this by integrating the electric field inside the sphere. Since $$E = 0$$ inside the sphere, $$V = constant$$ inside the sphere. What constant you might ask? Well, the potential has to have the same value inside the sphere as it does on the surface. This is where you need

$$V(R) = \frac{Q}{4\pi\epsilon_{0}R}$$

where $$R$$ is the radius of the sphere. Thus, the potential inside the sphere is a constant given by the above equation.

5. Sep 26, 2004

### ACLerok

thanks guys!

A potential difference of 5.25 kV is established between parallel plates in air.
If the air becomes electrically conducting when the electric field exceeds 3.1×106 V/m, what is the minimum separation of the plates?

What am i supposed to do for this question?

Last edited: Sep 26, 2004
6. Sep 26, 2004

### Staff: Mentor

The first thing you need to do is understand the relationship between electric field and potential. Look it up!

For a uniform field $\Delta V = - E_x \Delta x$.