Question

Calculate the net force acting on the charge present at the origin.

• A. $\frac{q q_{1}}{4 \pi \epsilon _{0} a^{2}}\times \sqrt{2}$
• B. $\frac{q q_{1}}{4 \pi \epsilon _{0} \sqrt{2} a^{2}}+\frac{q q_{1}}{8 \pi \epsilon _{0} a^{2}}$
• C. $\frac{q q_{1}}{4 \pi \left(\epsilon \right)_{0} a^{2}}\left(\right. \sqrt{2} + \frac{1}{2} \left.\right)$
• D. $\frac{q q_{1}}{4 \pi \left(\epsilon \right)_{0} a^{2}}\left(\right. \frac{1}{2} - \sqrt{2} \left.\right)$

Answer 1

Answer: (C)

$F_{1}=k\frac{q q_{1}}{a^{2}}; \, F_{2}=k\frac{q q_{1}}{\left(\right. \sqrt{2} a \left.\right)^{2}}$
Resultant force $F=\sqrt{2}F_{1}+F_{2}$
$=\sqrt{2}\frac{k q q_{1}}{a^{2}}+\frac{k q q_{1}}{2 a^{2}}$
$=\frac{k q q_{1}}{a^{2}}\left(\right. \sqrt{2} + \frac{1}{2} \left.\right)$
$=\frac{q q_{1}}{4 \pi \left(\epsilon \right)_{0} a^{2}}\left(\right. \sqrt{2} + \frac{1}{2} \left.\right)$