Two isolated metallic solid spheres of radii $$\mathrm{R}$$ and $$2 \mathrm{R}$$ are charged such that both have same charge density $$\sigma$$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $$\sigma^{\prime}$$. The ratio $$\frac{\sigma^{\prime}}{\sigma}$$ is :

A point charge $$2\times10^{-2}~\mathrm{C}$$ is moved from P to S in a uniform electric field of $$30~\mathrm{NC^{-1}}$$ directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be

In a cuboid of dimension $$2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}$$, a charge $$q$$ is placed at the center of the surface '$$\mathrm{S}$$' having area of $$4 \mathrm{~L}^{2}$$. The flux through the opposite surface to '$$\mathrm{S}$$' is given by

A point charge of 10 $$\mu$$C is placed at the origin. At what location on the X-axis should a point charge of 40 $$\mu$$C be placed so that the net electric field is zero at $$x=2$$cm on the X-axis?