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

Parnika Sharma
11 Points
5 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