The electrostatic potential inside a charged spherical ball is given by $\phi = ar^2 + b$ where $r$ is the distance from the centre $a,\,b$ are constants. Then the charge density inside the ball is
$ - \,6a{\varepsilon _0}r$
$ - \,24\pi a{\varepsilon _0}$
$ - \,6a{\varepsilon _0}$
$ - \,24\pi a{\varepsilon _0}r$
A parallel plate capacitor with air between the plates has a capacitance of $9\ pF$. The separation between its plates is '$d$'. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac{2d}{3}$. Capacitance of the capacitor is now........$pF$
A charge $q$ is placed at the centre of cubical box of side a with top open. The flux of the electricn field through one of the surface of the cubical box is
Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium, the value of $q$ is
A given charge is situated at a certain distance from an electric dipole in the axial position experiences a force $F$ . If the distance of the charge is doubled, the force acting on the charge will be
If potential at centre of uniformaly charged ring is $V_0$ then electric field at its centre will be (assume radius $=R$ )