First slide

Electric field

Question

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

Moderate

A

9000 N
B

12000 N
C

24000 N
D

36000 N

Solution

The schematic diagram of distribution of charges on x-axis is shown in figure below.
Total force acting on 1 C charge is given by
$\begin{array}{l} F = \frac{1}{4 {πε}_{o}} [\frac{1 \times 1 \times 10^{- 6}}{{(1)}^{2}} + \frac{1 \times 1 \times 10^{- 6}}{{(2)}^{2}} + \frac{1 \times 1 \times 10^{- 6}}{{(4)}^{2}} \frac{1 \times 1 \times 10^{- 6}}{{(8)}^{2}} + . .. \infty] \\ = \frac{10^{- 6}}{4 {πε}_{o}} (\frac{1}{1} + \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + . .. \infty) \\ = 9 \times 10^{9} \times 10^{- 6} (\frac{1}{1 - \frac{1}{4}}) \\ = 9 \times 10^{9} \times 10^{- 6} \times \frac{4}{3} = 9 \times 10^{3} \times \frac{4}{3} = 12000 N \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App