Question

Charge A has a charge of +2C. Charge B has a charge of -3C and is located 1 meter to the right of A. Charge C is located 1 meter to the right of Charge B and has a charge of -1C. If a fourth charge (Charge D) is placed 4 meters to the right of Charge B, how much charge must it have for the Net Force on Charge B to be zero?

Answer 1

If the net force on Charge B is zero, => the electric field strength is zero at the point B (charge B location).
vector E(A) +vector E(C) +vector E(D) = 0 =>
At the point B:
Vectors E(A) and E(C) are direcred to the right =>
vector E(D) has to be directed to the left => charge D is positive.

kq(A)/r(AB)²+ kq(C)/r(BC)²= kq(D)/r(BD)²
2/1²+ 1/1² =q(D)/4²
q(D) = + 48 C