Question

A uniformly charged rod (with total charge Q) and length l applies a force on other charge Q¹placed on its axis (i.e. along the rod) at a distance 1000l from its centre can be approximated as $\frac{KQ{Q}^1}{(1000l{)}^2}$ The reason it came out to be so is because

• A. charges are conserved
• B. charge is quantized
• C. charges are invariant in nature
• D. For such large distances, the rod can be considered as a point charge

Answer 1

The correct option is D

For such large distances, the rod can be considered as a point charge

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 try the derivation once and then watch the derivation video once again!

Now as you see in the equation as r becomes larger and larger

$r^2-L^2$ / 4goes closer and closer to $r^2$ and the line of charge behaves like a point charge. Here as r =1000L (much greater than L) E = $\frac{KQ{Q}^1}{(1000l{)}^2}$