Question

Infinite charges of magnitude q each are lying at x = 1, 2, 4, 8 ... metre on X-axis. The value of the intensity of the electric field at point x = 0 due to these charges will be ______

Options

• 12 x 10⁹ q N/C

• Zero

• 6 x 10⁹ q N/C

• 4 x 10⁹ q N/C

Answer 1

Infinite charges of magnitude q each are lying at x = 1, 2, 4, 8 ... metre on X-axis. The value of the intensity of the electric field at point x = 0 due to these charges will be 12 x 10⁹ q N/C.

Explanation:

The net field at the origin

E = `"q"/(4piepsilon_0)[1/1^2 + 1/2^2 + 1/4^2 + ....∞]`

= `"q"/(4piepsilon_0)[1 + 1/4 + 1/16 + ....∞]`

= `"q"/(4piepsilon_0)[1/(1 - 1/4)] = 12 xx 10^9` q N/C