Electrostatics

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?

An electric dipole of dipole moment $6 \times 10^{-6} \mathrm{Cm}$ is placed in uniform electric field of magnitude $10^{6} \mathrm{V} / \mathrm{m}$. Initially, the dipole moment is parallel to electric field. The work that needs to be done...

A square loop of sides $a=1 \mathrm{~m}$ is held normally in front of a point charge $\mathrm{q}=1 \mathrm{C}$ at a distance $\frac{\mathrm{a}}{2}$. The flux of the electric field through the shaded region is $\frac{5}{\mathrm{p}} \times \f...

Consider a parallel plate capacitor of area A (of each plate) and separation ' $d$ ' between the plates. If $E$ is the electric field and $\varepsilon_0$ is the permittivity of free space between the plates, then potential energy stored in ...

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 p...

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 $9 \times 10^{-3} \mathrm{~N}$...

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 mad...

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

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19} \mathrm{C}$ and $9.6 \times 10^{-10} \mathrm{C}$, and masses $19.2 \times 10^{-27} \mathrm{~kg}$ and $9 \times 10^{-27} \mathrm{~kg}$ respectively. At an instant, t...

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, $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$, the electrostat...

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 ...

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 tota...

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 poten...

At the centre of a half ring of radius \(\mathrm{R}=10 \mathrm{~cm}\) and linear charge density \(4 \mathrm{~nC} \mathrm{~m}^{-1}\), the potential is \(x \pi \mathrm{V}\). The value of \(x\) is _________.

An electric field \(\vec{E}=(2 x \hat{i}) N C^{-1}\) exists in space. A cube of side \(2 \mathrm{~m}\) is placed in the space as per figure given below. The electric flux through the cube is ______ \(\mathrm{Nm}^2 / \mathrm{C}\).

Five charges \(+q,+5 q,-2 q,+3 q\) and \(-4 q\) are situated as shown in the figure. The electric flux due to this configuration through the surface \(S\) is :

An electric field, \(\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}\) passes through the surface of \(4 \mathrm{~m}^2\) area having unit vector \(\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)\)....

Two charged conducting spheres of radii \(a\) and \(b\) are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

If the net electric field at point \(\mathrm{P}\) along \(\mathrm{Y}\) axis is zero, then the ratio of \(\left|\frac{q_2}{q_3}\right|\) is \(\frac{8}{5 \sqrt{x}}\), where \(x=\) ________.

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point \(P\) is \(\frac{x \sigma}{\epsilon_0}\). The value of \(x\) is _________ (all quantities are measured in SI units).

\(\sigma\) is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is :

Two identical conducting spheres P and S with charge Q on each, repel each other with a force \(16 \mathrm{~N}\). A third identical uncharged conducting sphere \(\mathrm{R}\) is successively brought in contact with the two spheres. The new ...

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

The electric field at point \(\mathrm{p}\) due to an electric dipole is \(\mathrm{E}\). The electric field at point \(\mathrm{R}\) on equitorial line will be \(\frac{\mathrm{E}}{x}\). The value of \(x\) :

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

An infinitely long positively charged straight thread has a linear charge density \(\lambda \mathrm{~Cm}^{-1}\). An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the va...

An infinite plane sheet of charge having uniform surface charge density \(+\sigma_{\mathrm{s}} \mathrm{C} / \mathrm{m}^2\) is placed on \(x\)-\(y\) plane. Another infinitely long line charge having uniform linear charge density $$+\lambda_e...

A charge \(q\) is placed at the center of one of the surface of a cube. The flux linked with the cube is:

Two charges \(q\) and \(3 q\) are separated by a distance '\(r\)' in air. At a distance \(x\) from charge \(q\), the resultant electric field is zero. The value of \(x\) is :

The distance between charges \(+q\) and \(-q\) is \(2 l\) and between \(+2 q\) and \(-2 q\) is \(4 l\). The electrostatic potential at point \(P\) at a distance \(r\) from center \(O\) is $$-\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \m...

Force between two point charges \(q_1\) and \(q_2\) placed in vacuum at '\(r\)' cm apart is \(F\). Force between them when placed in a medium having dielectric constant \(K=5\) at '\(r / 5\)' \(\mathrm{cm}\) apart will be:

The electrostatic potential due to an electric dipole at a distance '\(r\)' varies as :

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of \(37^{\circ}\) with each other. When suspended in a liquid of density \(0.7 \mathrm{~g} / \mathrm{cm}^3\), the angle remains same. If dens...

A particle of charge '\(-q\)' and mass '\(m\)' moves in a circle of radius '\(r\)' around an infinitely long line charge of linear charge density '\(+\lambda\)'. Then time period will be given as :
(Consider \(k\) as Coulomb's constant)

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet \(\mathrm{S}\) having surface charge density \(+\sigma\). The electron at \(t=0\) is at a distance of \(1 \mathrm{~m}\) from \(S\) a...

Two charges of \(5 Q\) and \(-2 Q\) are situated at the points \((3 a, 0)\) and \((-5 a, 0)\) respectively. The electric flux through a sphere of radius '\(4 a\)' having center at origin is :

An electric field is given by \((6 \hat{i}+5 \hat{j}+3 \hat{k}) \mathrm{N} / \mathrm{C}\). The electric flux through a surface area \(30 \hat{i} \mathrm{~m}^2\) lying in YZ-plane (in SI unit) is :

A thin metallic wire having cross sectional area of \(10^{-4} \mathrm{~m}^2\) is used to make a ring of radius \(30 \mathrm{~cm}\). A positive charge of \(2 \pi \mathrm{~C}\) is uniformly distributed over the ring, while another positive ch...

An electric charge \(10^{-6} \mu \mathrm{C}\) is placed at origin \((0,0)\) \(\mathrm{m}\) of \(\mathrm{X}-\mathrm{Y}\) co-ordinate system. Two points \(\mathrm{P}\) and \(\mathrm{Q}\) are situated at \((\sqrt{3}, \sqrt{3}) \mathrm{m}\) and...

The electric potential at the surface of an atomic nucleus \((z=50)\) of radius \(9 \times 10^{-13} \mathrm{~cm}\) is __________ \(\times 10^6 \mathrm{~V}\).

Two charges of \(-4 \mu \mathrm{C}\) and \(+4 \mu \mathrm{C}\) are placed at the points \(\mathrm{A}(1,0,4) \mathrm{m}\) and \(\mathrm{B}(2,-1,5) \mathrm{m}\) located in an electric field $$\overrightarrow{\mathrm{E}}=0.20 \hat{i} \mathrm{~...

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero.
Reason (R) : Elec...

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5 \mathrm{~g} / ...

Suppose a uniformly charged wall provides a uniform electric field of $2 \times 10^4 \mathrm{~N} / \mathrm{C}$ normally. A charged particle of mass $2 \mathrm{~g}$ being suspended through a silk thread of length $20 \mathrm{~cm}$ and remain...

$C_1$ and $C_2$ are two hollow concentric cubes enclosing charges $2 Q$ and $3 Q$ respectively as shown in figure. The ratio of electric flux passing through $C_1$ and $C_2$ is :

An electric dipole of dipole moment is \(6.0 \times 10^{-6} ~\mathrm{C m}\) placed in a uniform electric field of \(1.5 \times 10^{3} ~\mathrm{NC}^{-1}\) in such a way that dipole moment is along electric field. The work done in rotating di...

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius \(\mathrm{R}\), with distance \(r\) from the centre O is represented by:

Electric potential at a point '\(\mathrm{P}\)' due to a point charge of \(5 \times 10^{-9} \mathrm{C}\) is \(50 \mathrm{~V}\). The distance of '\(\mathrm{P}\)' from the point charge is:
(Assume, $$\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10...

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the centre (O) of shell can be graphically represented as -

A dipole comprises of two charged particles of identical magnitude \(q\) and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance...