Question

A charge Q is distributed uniformly along a rod of lengths L. The electric field at a distance ‘d’ along its axis from its closer end will be

• A. $\frac{KQ}{d^2}$
• B. $\frac{KQ}{d^2+dL}$
• C. $\frac{KQ}{d^2+\frac{L^2}{4}}$
• D. None of these

Answer 1

The correct option is B

$\frac{KQ}{d^2+dL}$

Alright! So the electric field due to a line of charge of length L at a point on its axis, at a distance r from the Centre of the rod is

$E=\frac{KQ}{r^2-L^2/4}$

If you don’t remember this then it’s okay! You don’t have to mug stuff up. I recommend you to watch try the derivation once and then watch the derivation video once again!

here the value of r is d + $\frac{L}{2}$ (as r is the distance from the Centre). Substituting that in the aforementioned equation we get

$E=\frac{KQ}{d^2+dL}$