Infinite charges of magnitude q each are lyin | vedclass

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Question

(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]

Vedclass · Accepted Answer

$12 	imes 10^9 q N/C$

Vedclass · Answer

(a) Net field at origin $E = \frac{q}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{{1^2}}} + \frac{1}{{{2^2}}} + \frac{1}{{{4^2}}} + ....\infty } ight]$
$ = \frac{q}{{4\pi {\varepsilon _0}}}\left[ {1 + \frac{1}{4} + \frac{1}{{16}} + .....\infty } ight]$
$ = \frac{q}{{4\pi {\varepsilon _0}}}\left[ {\frac{1}{{1 - \frac{1}{4}}}} ight] = 12 	imes {10^9}q\,N/C$

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

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