Question

Three point charges q1, q2 and q3 are located at the corners of an equilateral triangle with sides of 10 cm. The electrical forces between them are F12= 5.4 N (attractive), F13= 15 N (repulsive) and F23= 9 N (attractive). Given that q1 is negative, what are the values of q2 and q3?

(Answer: q2= 1.89 μC and q3= -5.28 μC)

Answer 1

Gives

$F_{12}=5.4N$

$F_{13}=15N$

$F_{23}=9N$

Now

$F_{13}=\frac{kq_1q_3}{r^2}$

$15=\frac{9\times10^9\times q_1\times q_3}{10^{-2}}$

$q_1q_3=1.66\times10^{-11}\rightarrow(1)$

$F_{12}=\frac{kq_1q_2}{r^2}$

$-5.4=\frac{9\times10^{9}q_1q_2}{10^{-2}}\\q_1q_2=-6\times10^{-12}\rightarrow(2)$

$F_{23}=\frac{kq_2q_3}{r^2}$

$q_2q_3=-1\times10^{-12}\rightarrow(3)$

$Equation (2) divided by(3)$

$\frac{q_1}{q_3}=-6$

$q_1=-6q_3$

Equation (1) put value

$$6q_3^2=-1.66\times10^{-10}\\q_3=-5.28\times10^{-6}C=-5.28\mu C$$

Equation (3) put $q_3$ Value

$$-5.28\times10^{-6}\times q_2=-1\times10^{-12}$$

$q_2=1.89\times10^{-6}=1.89\mu C$