#### Calculating the net field by vector addition

Consider the three equal-magnitude charges shown, placed at the corners of an equilateral triangle. The charge at the top vertex of the triangle is negative. The other two charges are positive.

What direction is the net electric field at point A, halfway between the two positive charges?

- up
- down
- left
- right
- other

At point A the fields from the positive charges cancel one another. The net field there comes from the negative charge only, and the field from a negative charge points toward the charge. The net field is directed up.

Imagine an infinitely long vertical line passing through point A and the negative charge. Is the net field equal to zero anywhere on this line a finite distance from the charges? If so, where is the field zero?

- At some point above the negative charge
- At some point between the negative charge and point A
- At some point below point A
- Both 1 and 3
- Both 2 and 3

We can rule out option 2, because the field everywhere between point A and the negative charge is directed up. At A the field is up, but at some point below A the positive charges take over and the field switches direction to down, away from the positive charges. Switching direction here implies that the field goes through zero at some point below A.

There is a similar point above the negative charge where the field is zero. Close to the negative charge the field points down, but as you get further away the positive charges take over and the field switches direction to up.