Two identical charged spheres suspended from a common point by two massless strings of length $$l$$ are initially a distance $$d\left( {d < < 1} \right)$$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $$v$$. Then as a function of distance $$x$$ between them,

The electrostatic potential inside a charged spherical ball is given by $$\phi = a{r^2} + b$$ where $$r$$ is the distance from the center and $$a,b$$ are constants. Then the charge density inside the ball is:

If a wire is stretched to make it $$0.1\% $$ longer, its resistance will:

A current $$I$$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $$R.$$ The magnitude of the magnetic induction along its axis is: