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Q.

An infinite number of electric charges each equal to 5 nano - coulombs are placed along X - axis at x = 1 cm , x = 2 cm , x = 4 cm , x = 8 cm .............. and so on. Then the electric field at x = 0 $(\frac{1}{4 π ε_{0}} = 9 \times 10^{9} N - m^{2} / c^{2})$

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a

$12 \times 10^{4} N / C$

b

$60 \times 10^{4} N / C$

c

$24 \times 10^{4} N / C$

d

$48 \times 10^{4} N / C$

answer is C.

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Detailed Solution

$\begin{matrix} E = \frac{1}{4 π \in_{0}} [\frac{q}{1^{2}} + \frac{q}{2^{2}} + \frac{q}{4^{2}} + ..........] \times \frac{1}{10^{- 4}} \\ = \frac{5 \times 10^{- 9} \times 9 \times 10^{9}}{10^{- 4}} \times \frac{1}{1 - \frac{1}{4}} = 60 \times 10^{4} \frac{N}{c} \end{matrix}$

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