A point charge causes an electric flux of $-2\times 10^4{\mathrm{Nm}}^2{\mathrm{C}}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given ${ϵ}_0=8.85\times 10^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$ )

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density ${\sigma }_{\mathrm{o}}$. Choose the correct option from the following.

An electric dipole of mass $m$, charge $q$, and length $l$ is placed in a uniform electric field $\vec{E}=E_0\hat{i}$. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

A line charge of length $\frac{\mathrm{a}}{2}$ is kept at the center of an edge $B C$ of a cube ABCDEFGH having edge length ' $a$ ' as shown in the figure. If the density of line charge is $\lambda \mathrm{C}$ per unit length, then the total electric flux through all the faces of the cube will be ___________ . (Take, ${ϵ}_0$ as the free space permittivity)

Match List - I with List - II. List - I List - II (A) Electric field inside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (I) σ/ε0 (B) Electric field at distance r>0 from a uniformly charged infinite plane sheet with surface charge density σ. (II) σ/2ε0 (C) Electric field outside (distance r>0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (III) 0 (D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density σ. (IV) $\frac{\sigma }{{ϵ}_0{r}^2}$ Choose the correct answer from the options given below :

For a short dipole placed at origin O , the dipole moment P is along $x$-axis, as shown in the figure. If the electric potential and electric field at $A$ are $V_0$ and $E_0$, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the $y$-axis is given by

A point particle of charge $Q$ is located at $P$ along the axis of an electric dipole 1 at a distance $r$ as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance $2 a$. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

The electric flux is $\varphi =\alpha \sigma +\beta \lambda$ where $\lambda$ and $\sigma$ are linear and surface charge density, respectively. $\left(\frac{\alpha }{\beta }\right)$ represents

Two point charges $-4\mu \mathrm{c}$ and $4\mu \mathrm{c}$, constituting an electric dipole, are placed at $(-9,0,0)\mathrm{cm}$ and $(9,0,0)\mathrm{cm}$ in a uniform electric field of strength $10^4{\mathrm{NC}}^{-1}$. The work done on the dipole in rotating it from the equilibrium through $180^{\circ }$ is :

Two charges $7\mu \mathrm{c}$ and $-4\mu \mathrm{c}$ are placed at $(-7\mathrm{cm},0,0)$ and $(7\mathrm{cm},0,0)$ respectively. Given, ${ϵ}_0=8.85\times 10^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}$, the electrostatic potential energy of the charge configuration is :

Consider a parallel plate capacitor of area A (of each plate) and separation ' $d$ ' between the plates. If $E$ is the electric field and ${\epsilon }_0$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4\times 10^{-8}\mathrm{C}$ charge and then removed to a distance such that the force of repulsion between them is $9\times 10^{-3}\mathrm{N}$. The distance between them is (Take $\frac{1}{4\pi {ϵ}_{\mathrm{o}}}$ as $9\times 10^9$ in SI units)

In the first configuration (1) as shown in the figure, four identical charges $\left(q_0\right)$ are kept at the corners A, B, C and D of square of side length ' $a$ '. In the second configuration (2), the same charges are shifted to mid points $G, E, H$ and $F$, of the square. If $K=\frac{1}{4\pi {ϵ}_0}$, the difference between the potential energies of configuration (2) and (1) is given by :

Three infinitely long wires with linear charge density $\lambda$ are placed along the $x-a x i s, y-a x i s$ and $z-$ axis respectively. Which of the following denotes an equipotential surface?

A particle of mass ' $m$ ' and charge ' $q$ ' is fastened to one end ' $A$ ' of a massless string having equilibrium length $l$, whose other end is fixed at point ' $O$ '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the $x$-axis is

Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ1 and σ2, respectively. The ratio $\frac{{\sigma }_1}{{\sigma }_2}$ is

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. Reason R : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below.

Electric charge is transferred to an irregular metallic disk as shown in the figure. If ${\sigma }_1$, ${\sigma }_2$, ${\sigma }_3$ and ${\sigma }_4$ are charge densities at given points then, choose the correct answer from the options given below: A. ${\sigma }_1>{\sigma }_3;{\sigma }_2={\sigma }_4$ B. ${\sigma }_1>{\sigma }_2;{\sigma }_3>{\sigma }_4$ C. ${\sigma }_1>{\sigma }_3>{\sigma }_2={\sigma }_4$ D. ${\sigma }_1<{\sigma }_3<{\sigma }_2={\sigma }_4$ E. ${\sigma }_1={\sigma }_2={\sigma }_3={\sigma }_4$

An infinitely long wire has uniform linear charge density $\lambda =2\text{ nC/m}$. The net flux through a Gaussian cube of side length $\sqrt{3}$ cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $x{\text{ Nm}}^2{\text{C}}^{-1}$, where $x$ is: [Neglect any edge effects and use $\frac{1}{4\pi {ϵ}_0}=9\times 10^9$ SI units]

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+\sigma$ and $-2\sigma$. The force experienced by a point charge +q placed at the mid point between two plates will be: