Two concentric spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is
$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non uniformly distributed on $A$
$A$ and $C$
$A$ and $D$
$B$ and $C$
$B$ and $D$
If the distance between two equal point charge is doubled then what would happen to the force between them ?
In steady state heat conduction, the equations that determine the heat current $j ( r )$ [heat flowing per unit time per unit area] and temperature $T( r )$ in space are exactly the same as those governing the electric field $E ( r )$ and electrostatic potential $V( r )$ with the equivalence given in the table below.
Heat flow | Electrostatics |
$T( r )$ | $V( r )$ |
$j ( r )$ | $E ( r )$ |
We exploit this equivalence to predict the rate $Q$ of total heat flowing by conduction from the surfaces of spheres of varying radii, all maintained at the same temperature. If $\dot{Q} \propto R^{n}$, where $R$ is the radius, then the value of $n$ is
The electric potential $V$ at any point $(x, y, z)$ (all in $metres$ ) in space is given by $V = 4x^2\, volt$. The electric field at the point $(1\, m, 0, 2\, m)$ in $volt/metre$ is
Two point charges $+q$ and $-q$ are held fixed at $(-d, 0)$ and $(+d, 0)$ respectively of a $(x, y)$ coordinate system. Then
The potential $V$ is varying with $x$ and $y$ as $V = \frac{1}{2}({y^2} - 4x)\,volts$ The field at $(1\,m,\,1\,m)$ is