Question

10 charges having charge 1 micro columb, 8 micro columb, 27 micro columb ...............1000 micro columb are placed on x axis with coordinates x=1m, 2m, 3m, 4m, ........10m. The net electric field intensity at the origin is

Answer 1

Electric field due to a point charge at a distance r is KQ/r².
The net electric field at the origin is K×1³μ/1² + K×2³μ/2² + K×3³μ/3² .... + K×10³μ/10² = μ(K + 2K + 3K + ... + 10K) = 55×10⁻⁶×9×10⁹ = 4.95×10⁵ N/C.

Answer 2

"The "net electric field" intensity at the origin is $4.95 \times 10^{5} \mathrm{N} / \mathrm{C}$

Solution:

Given,

10 charges having charge 1 micro columb, 8 micro columb, 27 micro columb ...............1000 micro columb are placed on x axis with coordinates x=1m, 2m, 3m, 4m, ........10m.

"Electric field" due to a "point charge" at a distance r is given by the$\frac {KQ}{ r²} .$

The net electric field at the origin is,

$={ \frac { K\times 1^{ 3 }\mu}{ 1^{ 2 }}}+\frac { { K }\times 2^{ 3}\mu}{ 2^{ 2 }} +\frac { { K }\times 3^{ 3 }\mu}{ 3^{ 2 }} +\frac { { K }\times 10^{ 3 }\mu}{ 10^{ 2 } } =\mu ({ K }+2{ K }+3{ K }+10{ K })$

$=55 \times 10^{-6} \times 9 \times 10^{9}$

$=4.95 \times 10^{5} \mathrm{N} / \mathrm{C}$"