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An infinite number of charges each 4 micro coloumb are placed along x axis at X=1,X=2,X=4,X=8 SO ON field at orgine all of them

An infinite number of charges each 4 micro coloumb are placed along x axis at X=1,X=2,X=4,X=8 SO ON field at orgine all of them

Grade:12

1 Answers

Parnika Sharma
11 Points
4 years ago
Electric field due to each of the charges will be in the same direction, so net electric field will be the sum of all individual fields.
\frac{q}{4\pi \varepsilon } [\frac{1}{1^{2}} + \frac{1}{2^{2}} + \frac{1}{4^{2}} ..]
The sum of the infinite GP is 
\frac{a}{1 - r}
 
So we get \frac{q}{4\pi \varepsilon } [\frac{1}{1 - 1/4}]
 
Putting the given values 
4 \times 10^{-6} \times 9 \times 10^{9} \times \frac{4}{3}
4.8 \times 10^{4} N/C 
towards the negative x direction

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