$n$ small drops of same size are charged to $V$ $volts$ each. If they coalesce to form a signal large drop, then its potential will be
$V/n$
$Vn$
$Vn^{1/3}$
$Vn^{2/3}$
A sphere of radius $R$ and charge $Q$ is placed inside an imaginary sphere of radius $2R$ whose centre coincides with the given sphere. The flux related to imaginary sphere is
In a particle accelerator, a current of $500 \,\mu A$ is carried by a proton beam in which each proton has a speed of $3 \times 10^7 \,m / s$. The cross-sectional area of the beam is $1.50 \,mm ^2$. The charge density in this beam (in $C / m ^3$ ) is close to
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
If potential at centre of uniformaly charged ring is $V_0$ then electric field at its centre will be (assume radius $=R$ )
A hollow cylinder has charge $q$ $C$ within it. If $\phi $ is the electric flux in unit of voltmeter associated with the curved surface $B$, the flux linked with the plane surface $A$ in unit of voltmeter will be