Question

A charge is distributed along an infinite curved line in space with linear charge distribution λ. What will be the amount of force on a point charge q kept at a certain distance from the line?

(a) q∫\(\frac {\lambda}{r^2}\hat{r}\)dl

(b) q∫\(\frac {\lambda}{r^2}\hat{r}\)dr

(c) q∫\(\frac {\lambda}{r^3}\hat{r}\)dl

(d) q∫\(\frac {\lambda}{r^2}\)

I have been asked this question in an internship interview.

Query is from Continuous Charge Distribution topic in section Charges and Fields of Physics – Class 12

Answer 1

Correct choice is (a) q∫\(\frac {\lambda}{r^2}\hat{r}\)dl

The best explanation: Let the point charge is situated at a distance r from a small part dl on the line. The charge stored in stat small part=λ.dl. The force due to that small part will be directed towards the unit vector \(\hat{r}\). Therefore, force on that charge due to the entire linear charge distribution=q∫\(\frac {\lambda}{r^2}\hat{r}\)dl.