# Electric Potential problem

1. Mar 5, 2012

### Biosyn

1. The problem statement, all variables and given/known data

A charge of +9q is fixed to one corner of a square, while a charge of -8q is fixed to the opposite corner. Expressed in terms of q, what charge should be fixed to the center of the square, so the potential is zero at each of the two empty corners?

2. Relevant equations

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

3. The attempt at a solution

q1 = charge that should be fixed to center

d = distance between the two positive charges
The distance that the charge in the center of the square is from the two other charges is: d√2

$\frac{k(+9q)}{d}$ + $\frac{k(-8q)}{d}$ + $\frac{k(q1)}{d√2}$ = 0

$\frac{k(+9q-8q)}{d}$ + $\frac{k(q1)}{d√2}$ = 0

$\frac{k(+9q-8q)}{d}$ = -$\frac{k(q1)}{d√2}$

q1 = -q√2

The answer in the back of the book is $-q/√2$

2. Mar 5, 2012

### SammyS

Staff Emeritus
"The distance that the charge in the center of the square is from the two other charges is: d√2 ."

d√2 > d . How can that be?

What you really want is the distance from q1 to the two empty corners of the square. (Of course that is equal to the distance from q1 to each of the two other charges.)

3. Mar 5, 2012

### Biosyn

Would that distance be .5d√2 ?

I'm not really sure how to set up an equation for this problem..

4. Mar 5, 2012

### SammyS

Staff Emeritus
Yes, that's the distance.

5. Mar 5, 2012

### Biosyn

Would the equation be this? :/

$\frac{k(+9q)}{d}$ + $\frac{k(-8q)}{d}$ + $\frac{k(q1)}{.5d√2}$ = 0

I get q1 = $\frac{-q√2}{2}$

Last edited: Mar 5, 2012