Answer to Question #87938 in Electricity and Magnetism for Merl

Question

Three charged objects are placed as follows: Object B (1.5mC), object R (2.0mC), and object L (unknown). The distance between B and R is the same as the distance between the R and L. If the force on R is zero, what is the charge on L?

Answer 1

$$F_{RB}=\frac{lq_Rq_B}{d^2}$$

$$F_{RL}=\frac{lq_Rq_L}{d^2}$$

If the force on R is zero,

$$F_{RB}=F_{RL}\implies\frac{lq_Rq_L}{d^2}=\frac{lq_Rq_B}{d^2}$$

Thus,

$$q_L=q_B=1.5mC$$