# Electrostatics question

1. Jul 30, 2016

### Clara Chung

1. The problem statement, all variables and given/known data
Four point charges are placed at the corners of a square of side 1m as shown in Fig 18.54 Find
a) the electric field, and
b) the electric potential at the center of the square

Photo is attached
2. Relevant equations
coulomb's law
Ans of a=76.3 x 10^3 NC^-1 upward
Ans of b=-25.4x 10^3 V
3. The attempt at a solution
I can do part a by 2x(2/10^6)x2x8.99x10^9xsin45 + 2x(2/10^6)x8.99x10^9xsin45=76.3 x 10^3 NC^-1 upward.
I just attempted b part by 2x(2/10^6)xroot2x8.99x10^9xsin45 + 2x(1/10^6)xroot2x8.99x10^9xsin45
because V=ED I just multiply each term by its length 1/root2 from the center.
But the answer seems to be one third of the answer from part a, please teach me how to do.

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2. Jul 30, 2016

### Simon Bridge

Try doing it from the definition of the electric potential.

3. Jul 30, 2016

### Clara Chung

Use the definition: work done per charge from infinity to the center?

4. Jul 30, 2016

### cnh1995

That will work. Potential at a point at a distance r due to a charge q is kq/r. You can add and subtract potentials aglebraically.

5. Jul 30, 2016

### Clara Chung

Thanks I forget that voltage is scalar

6. Jul 30, 2016

Well done.