Answer to Question #177475 in Electricity and Magnetism for Moon

Question

Three point charges are arranged on a line. Charge q3 = +5.00 nC and is at the origin.

Charge q2 = -3.00 nC and is at x = +4.00 cm. Charge q1 is at x = +2.00 cm. What is q1

(magnitude and sign) if the net force on q3 is zero?

Answer 1

$\bar{F}_{2,3}=k \frac{|q_2q_3|}{r^2_{2,3}} ; \bar{F}_{1,3}=k \frac{|q_1q_3|}{r^2_{1,3}}$

$\bar{F}_{2,3}$ point in the x-direction, so wee need $\bar{F}_{1,3}$ to point in the - x direction. Thus q₁ must have a positive charge. We set the two forces equal

$k \frac{|q_2q_3|}{r^2_{2,3}} =k \frac{|q_1q_3|}{r^2_{1,3}}$

$|q_1|=|q_2| \frac{r^2_{1,3}}{r^2_{2,3}}$

$|q_1|=|-3nC| \times \frac{2^2}{4^2}$

$|q_1|=3\times \frac{2^2}{4^2} nC$

$|q_1|= 0.75 nC$

$q_1= +0.75 nC$