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1. Electric Charges and Fields
medium
Infinite charges of magnitude $q$ each are lying at $x =1,\, 2,\, 4,\, 8...$ meter on $X$-axis. The value of intensity of electric field at point $x = 0$ due to these charges will be
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
(a) Net field at origin $E = \frac{q}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{1^2}}} + \frac{1}{{{2^2}}} + \frac{1}{{{4^2}}} + ….\infty } \right]$
$ = \frac{q}{{4\pi {\varepsilon _0}}}\left[ {1 + \frac{1}{4} + \frac{1}{{16}} + …..\infty } \right]$
$ = \frac{q}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{1 – \frac{1}{4}}}} \right] = 12 \times {10^9}q\,N/C$
Standard 12
Physics
