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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»

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.



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