Question

A point moves so that the sum of the squares of its distances from the six faces of a cube given by x=1, y =1, z=1 is 10 units, then locus of the point is

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)