Answer to Question #291155 in Electricity and Magnetism for Ase

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

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

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