A conducting sphere of radius $R$ is given a charge $Q.$ The electric potential and the electric field at the center of the sphere respectively are

In a region the potential is represented by $V(x, y, z) = 6x - 8xy - 8y + 6yz.$ The electric force experienced by a charge of 2 C situated at point $(1,1,1)$ is

A parallel plate air capacitor of capacitance $C$ is connected to a cell of emf $V$ and then disconnected from it. A dielectric slab of dielectric constant $K,$ which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?

A capacitor of 2 μF is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of the resulting system:

The diagrams below show regions of equipotential. A positive charge is moved from A to B in each diagram.

The electrostatic force between the metal plates of an isolated parallel plate capacitor $C$ having a charge $Q$ and area $A,$ is

Which of the following acts as a circuit protection device?

The capacitance of a parallel plate capacitor with air as medium is $6 \mu F.$ With the introduction of a dielectric medium, the capacitance becomes $30 \mu F.$ The permittivity of the medium is:$\quad (\epsilon_0 = 8.85 \times 10^{-12}$ C$^2$ N$^{-1}$ m$^{-2})$

In a certain region of space with volume $0.2$ m$^3,$ the electric potential is found to be $5$ V throughout. The magnitude of electric field in this region is:

Polar molecules are the molecules:

A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and the area of each plate is $A,$ the energy stored in the capacitor is:$\newline (\varepsilon_0 =$permittivity of free space$)$

The equivalent capacitance of the combination shown in the figure is:

A dipole is placed in an electric field as shown. In which direction will it move?

Twenty-seven drops of same size are charged at $220$ V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

The angle between the electric lines of force and the equipotential surface is:

A capacitor of capacitance $C = 900 pF$ is charged fully by a $100V$ battery. Then the battery is disconnected, and the capacitor is connected to another uncharged capacitor of capacitance $C = 900 pF.$ The electrostatic energy stored by the system is:

Two hollow conducting spheres of radii $R_1$ and $R_2$ ($R_1 >> R_2$) have equal charges. The potential would be:

The equivalent capacitance of the system shown in the following circuit is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.$\newline \textbf{Assertion A:}$ The potential (V) at any axial point, at $2m$ distance $(r)$ from the centre of the dipole of dipole moment vector $\vec{P}$ of magnitude, $4 \times 10^{-6}$ C m, is $9 \times 10^3$V$\newline$Take $(\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9$ SI units$) \newline \textbf{Reason R:}$ $V = \frac{2P}{4\pi \varepsilon_0 r^2},$ where $r$ is the distance of any axial point, situated at $2m$ from the centre of the dipole.$$

A thin spherical shell is charged by some source. The potential difference between the two points C and P (in V) shown in the figure is:$\\ ( \frac{1}{4\pi \varepsilon_0} = 9 \times 10^9$ SI units$)$

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then:$\\ A.$ The charge stored in it, increases.$\\ B.$ The energy stored in it, decreases.$\\ C.$ Its capacitance increases.$\\ D.$ The ratio of charge to its potential remains the same.$\\ E.$ The product of charge and voltage increases.$\\$Choose the most appropriate answer from the options given below:

In the following circuit, the equivalent capacitance between terminal A and terminal B is: