- #1

Biosyn

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## Homework Statement

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?

## Homework Equations

V = [itex]\frac{kq}{r}[/itex]

## 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

[itex]\frac{k(+9q)}{d}[/itex] + [itex]\frac{k(-8q)}{d}[/itex] + [itex]\frac{k(q1)}{d√2}[/itex] = 0

[itex]\frac{k(+9q-8q)}{d}[/itex] + [itex]\frac{k(q1)}{d√2}[/itex] = 0

[itex]\frac{k(+9q-8q)}{d}[/itex] = -[itex]\frac{k(q1)}{d√2}[/itex]

q1 = -q√2 The answer in the back of the book is [itex]-q/√2[/itex]