# Electron Sphere and Magnitude

1. Jan 25, 2007

### stylez03

1. The problem statement, all variables and given/known data
Two small spheres spaced 20.0 cm apart have equal charge.

How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 4.57 * 10^-21 N?

2. Relevant equations
F = 1/4pi*e_o * k * (|Q1|*|Q2| / r^2)

1/4pi*e_o = 8.988 * 10^-9

3. The attempt at a solution

Since we know the force, we just have to find how many excess electrons and since they have the same charge, we can just take that value and square it.

4.57 * 10^21 = 8.988 * 10^-9 * ((x * 10^-9)^2 / (.20)^2)

I've tried different values of X but I can't seem to get it to equate to given Force, and I'm not sure if I'm doing it right anymore.

2. Jan 25, 2007

### Kurdt

Staff Emeritus
If you manipulate the equation before putting the numbers in then it will be a lot easier.

$$q^2 =\frac{r^2F}{k}$$

The square root will give you the charge on each sphere and then you will have to divide that by the charge on an electron to determine the number of electrons on the sphere.

3. Jan 26, 2007

### stylez03

q^2 = r^2*F / k

q = sqrt(r^2*F / k)

r = .20m
F = 4.57 * 10^-21
k = 8.85 * 10^-12

sqrt( ((.20)^2 * (4.57*10^-12)) / (8.85*10^-12) )

Doing the math I get q = .000005

You said to take this value and divide by the charge of an electron? I'm not sure what to do with this value after I obtain q, I know this should give you the charge of q right?

4. Jan 26, 2007

### Kurdt

Staff Emeritus
In the equation I gave you $$k=\frac{1}{4\pi \epsilon_0}$$ so the value you used is incorrect. As for q, that is the charge on 1 sphere and to find how many eectrons cause the charge you need to divide q by the charge on an electron.

5. Jan 26, 2007

### stylez03

Yes, you're right I must of have missed that.

From the new calculations:

sqrt( ((.20)^2 * (4.57*10^-12)) / (1/ 4*pi*(8.85*10^-12)) )

q = 1.42*10^-16

Charge of Electron = 1.602 × 10^-19

So you said take q / charge of electron?

(1.42*10^-16) / (1.602* 10^-19) = 8.9*10^-36?

I entered that in as the solution, but the online program says it's still incorrect.

Last edited: Jan 26, 2007
6. Jan 26, 2007

### Kurdt

Staff Emeritus
Should come out at about 890.

7. Jan 26, 2007