Question

An infinite number of charges, each of charge 1 $\mu C$ are placed on the x-axis with co-ordinates x = 1, 2, 4, 8, ......... $\infty$. If a charge of 1 C is kept at the origin, then what is the net force acting on 1 C charge

• A. 9000 N
• B. 12000 N
• C. 24000 N
• D. 36000 N

Answer 1

The correct option is B 12000 N

$\begin{array}{cc}F=\frac{1}{4\pi {\in }_0}\Sigma \frac{qiqj}{r^{2}ij}& \\ =9\times {10}^9\times {10}^{-6}\left[1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}......\right]& \\ =9\times {10}^3\left[\frac{1}{1-\frac{1}{4}}\right]& \left\{\because Sumof\propto G.P=\left(\frac{a}{1-r}\right)\right\}\\ =9\times {10}^3\times \frac{4}{3}=12000N& \end{array}$