First slide

Electric field

Question

Infinite charges of magnitude q each are lying at x =l , 2, 4, 8 ... meter on x-axis. The value of intensity of electric field at point x = 0 due to these charges will be

Moderate

A

$12 \times 10^{9} q N / C$
B

Zero
C

$6 \times 10^{9} q N / C$
D

$4 \times 10^{9} q N / C$

Solution

$Net field at origin, E = \frac{q}{4 {πε}_{0}} [\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{4^{2}} + \dots \infty] = \frac{q}{4 {πε}_{0}} [1 + \frac{1}{4} + \frac{1}{16} + \dots . . \infty] = \frac{q}{4 {πε}_{0}} [\frac{1}{1 - \frac{1}{4}}] = 12 \times 10^{9} q N / C$

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