Question

The drawing shows two point charges on the x axis. No other charges are nearby. Given that the net electric field E at location P, due to both charges, is 0 N/C, is the sign of the charge q₂ positive or negative? Explain.

There are no forces involved in the explanation, so using words like "attract" and "repel" is an indication that you're headed the wrong way. Also, there are no charges at location P.

q1= +5nC

Answer 1

Electric field is a vector quantity. Electric field due to q₁ = +5nC is given by,

E₁ = k * 5 * 10^-9 / r²      N/C    where k is the Coulomb's force constant and r the distance between q₁ and point P.

The direction of the field is towards the point P. Since the net field at point P is 0 N/C, there is an equal amount of field acting in "opposite" direction. If q₂ is negative, the direction of the field at point P will again be from point P to the charge, that is away from point P. This will not negate the field due to q₁ at P. So,

q₂ = + ve

This is essentially true if the point P is on the x-axis, and between the point charges q₁ and q₂.