Question

Hey!!!
________________________________________
A point charge q is situated at a distance d from one end of a thin non conducting rod of length l and charge q uniformly over its length find the magnitude of electric force between them.
________________________________________
Only answer if you know
Wrong answers will be deleted.

Answer 1

We know, coulombs law is valid only in case of point charge . But here we see charge varies with distance of point charge . So, we have to use integration method to find out electric field between them,

Cut an elementary length dx in rod at x distance from the point charge.
now, charge on element , dQ = (q/l)dx

Now, you can apply Coulombs law,
e.g., Electric force , F = KqdQ/x²
F $\bold{= \int\limits^{(d+l)}_d{\frac{K.q.(q/l)}{x^2},dx}}$ [∵dQ =n(q/l)dx
$\bold{=\frac{kq^2}{l} \int\limits^{(d+l)}_d{\frac{1}{x^2},dx}}$
= $=\bold{\frac{kq^2}{l}[\frac{-1}{x}]^{(d+l)}_d}$
= kq^2/d(d+l)

Hence, electric force between them is kq²/d(d+l)