Three point charges $$\mathrm{q},-2 \mathrm{q}$$ and $$\mathrm{q}$$ are placed along $$x$$ axis at $$x=-{a}, 0$$ and $a$ respectively. As $$\mathrm{a} \rightarrow 0$$ and $$\mathrm{q} \rightarrow \infty$$ while $$\mathrm{q} \mathrm{a}^2=\mathrm{Q}$$ remains finite, the electric field at a point P, at a distance $$x(x \gg a)$$ from $$x=0$$ is $$\overrightarrow{\mathrm{E}}=\frac{\alpha \mathrm{Q}}{4 \pi \epsilon_0 x^\beta} \hat{i}$$. Then

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,