A point charge of magnitude $+ 1\,\mu C$ is fixed at $(0, 0, 0) $. An isolated uncharged spherical conductor, is fixed with its center at $(4, 0, 0).$ The potential and the induced electric field at the centre of the sphere is

Electric charges having same magnitude of electricicharge $q$ coulombs are placed at $x=1 \,m , 2 \,m , 4 \,m$, $8 \,m$……. so on. If any two consecutive charges have opposite sign but the first charge is necessarily positive, what will be the potential at $x=0$ ?

If a charged spherical conductor of radius $10\,cm$ has potential $V$ at a point distant $5\,cm$ from its centre, then the potential at a point distant $15\,cm$ from the centre will be

The electric field in a region surrounding the origin is uniform and along the $x$ – axis. A small circle is drawn with the centre at the origin cutting the axes at points $A, B, C, D$ having co-ordinates $(a, 0), (0, a), (-a, 0), (0, -a)$; respectively as shown in figure then potential in minimum at the point

A thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $p$ at distance $\frac{R}{2}$ from the centre of the shell is