Question

Three charges $q_1=1\mu C,q_2=-2\mu C,q_3=2\mu C$, are placed at the vertices of an equilateral triangle of side 1m. The magnitude of net electric force in newton on charge $q_1$ is

• A. $13.92\times {10}^{-3}N$
• B. $18.0\times {10}^{-3}N$
• C. $12.93\times {10}^{-3}N$
• D. $11.23\times {10}^{-3}N$

Answer 1

The correct option is B $18.0\times {10}^{-3}N$


This problem is based on the principle of superposition of electric forces
$F_{13}=9\times {10}^9\frac{(1\times {10}^{-6})(2\times {10}^{-6})}{1^2}$
$=18\times {10}^{-3}$
$F_{12}=9\times {10}^4\frac{(1\times {10}^{-6})(2\times {10}^{-6})}{1^2}$
$=18\times {10}^{-3}$
$F_{net}$ on $q_1$ is F
$=\sqrt{(18\times {10}^{-3}{)}^2+(18\times {10}^{-3}{)}^2+2(18\times {10}^{-3}{)}^{2}cos{120}^{\circ }}$
$=18.0\times {10}^{-3}N$