Consider a positively charged infinite cylinder with uniform volume charge density $$\rho > 0$$. An electric dipole consisting of + Q and $$-$$ Q charges attached to opposite ends of a massless rod is oriented as shown in the figure. At the instant as shown in the figure, the dipole will experience,

A thin glass rod is bent in a semicircle of radius R. A charge is non-uniformly distributed along the rod with a linear charge density $$\lambda=\lambda_0\sin\theta$$ ($$\lambda_0$$ is a positive constant). The electric field at the centre P of the semicircle is,

The figure represents two equipotential lines in x-y plane for an electric field. The x-component E$$_x$$ of the electric field in space between these equipotential lines is,

An electric dipole of dipole moment $$\vec{p}$$ is placed at the origin of the co-ordinate system along the $$\mathrm{z}$$-axis. The amount of work required to move a charge '$$\mathrm{q}$$' from the point $$(\mathrm{a}, 0, 0)$$ to the point $$(0,0, a)$$ is,