Three point charges q , - 2 q and 2 q are placed on x axis at a distance x = 0 , x = 3 4 R and x = R respectively from origin as shown. If q = 2 × 10 - 6   C and R = 2   cm , the magnitude of net force experienced by the charge - 2 q is _____ N .

Question

Three point charges q , - 2 q and 2 q are placed on x axis at a distance x = 0 , x = 3 4 R and x = R respectively from origin as shown. If q = 2 &#215; 10 - 6 &#160; C and R = 2 &#160; cm , the magnitude of net force experienced by the charge - 2 q is _____ N .

Aicharya · Accepted Answer

The net force on the given charge will be the resultant of the forces due to the other two charges.
Hence, the net force $(F_{n})$ can be calculated as follows:
$\begin{array}{rcl} F_{n} & = & \frac{1}{4 π ε_{0}} \frac{4 q^{2}}{{(\frac{R}{4})}^{2}} - \frac{1}{4 π ε_{0}} \frac{2 q^{2}}{{(\frac{3 R}{4})}^{2}} \\ = & 9 \times 10^{9} \times \frac{16 q^{2}}{R^{2}} [4 - \frac{2}{9}] \\ = & 9 \times 10^{9} \times \frac{16 \times {(2 \times 10^{- 6} C)}^{2}}{{(0.02 m)}^{2}} \times \frac{34}{9} \\ = & 5440 N \end{array}$

Three point charges q , - 2 q and 2 q are placed on x axis at a distance x = 0 , x = 3 4 R and x = R…

Solution