At a distance of $5 \mathrm{cm}$ and $10 \mathrm{cm}$ outwards from the surface of a uniformly charged solid sphere, the potentials are $100 \mathrm{V}$ and $75 \mathrm{V}$, respectively. Then,

Four short dipoles, each of dipole moment $p$, are placed at the vertices of a square of side $a$. The direction of the dipole moments are shown in the figure.

Figure shows a charge $Q$ placed at the centre of the open face of a cylinder as shown in the figure. A second charge $q$ is placed at one of the positions $A, B, C$ and $D$, out of which positions $A$ and $D$ are lying on a straight line parallel to the open face of the cylinder. In which position(s) of this second charge, the flux of the electric field through the cylinder remains unchanged?

A long cylindrical volume (of radius $R$) contains a uniformly distributed charge of density $\rho$. Consider a point $P$ inside the cylindrical volume at a distance $x$ from its axis as shown in the figure. Here $x$ can be more than or less than $R$. Electric field at point $P$ is:

An imaginary closed surface $P$ is constructed around a neutral conducting wire connected to a battery and a switch as shown in the figure. As the switch is closed, the free electrons in the wire start moving along the wire. In any time interval, the number of electrons entering the closed surface $P$ is equal to the number of electrons leaving it. On closing the switch, the flux of the electric field through the closed surface:

$A$ and $B$ are two conducting concentric spherical shells. $A$ is given a charge $Q$ while $B$ is uncharged. If now $B$ is earthed as shown in figure.Then

A point charge $q$ is within an electrically neutral conducting shell whose outer surface is a sphere of radius $R$. The centre of outer surface is at $O$. Consider a point $P$ outside the conductor as shown in the figure. The magnitude of electric field at $P$