Electrostatics

Consider a long uniformly charged cylinder having constant volume charge density ' $\lambda$ ' and radius ' $R$ '. A Gaussian surface is in the form of a cylinder of radius ' $r$ ' such that vertical axis of both the cylinders coincide. For...

Charges of $2 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ are placed at two points A and B separated by 1 m . The distance of the point from A , where net potential is zero, is

In an electric field due to charge $Q$, a charge $q$ moves from point A to B as shown in the figure. The work done is ( $\varepsilon_0=$ permittivity of free space)

Two point charges $+q_1$ and $q_2$ repel each other with a force of $100 \mathrm{~N} . q_1$ is increased by $10 \%$ and $q_2$ is decreased by $10 \%$. If they are kept at their original positions the change in the force of repulsion between...

Charges $3 \mathrm{Q}, \mathrm{q}$ and Q are placed along x -axis at positions $\mathrm{x}=0, \mathrm{x}=\frac{1}{3}$ and $\mathrm{x}=1$ respectively. When the force on charge Q is zero, the value of $q$ is

A small particle carrying a negative charge of $1.6 \times 10^{-19} \mathrm{C}$ is suspended in equilibrium between two horizontal metal plates 8 cm apart having a potential difference of 980 V across them. The mass of the particle is $\lef...

The point charges $+\mathrm{q},-\mathrm{q},-\mathrm{q},+\mathrm{q},+\mathrm{Q}$ and -q are placed at the vertices of a regular hexagon ABCDEF as shown in figure. The electric field at the centre of hexagon ' $O$ ' due to the five charges at...

$A$ sphere ' $A$ ' of radius ' $R$ ' has a charge ' $Q$ ' on it. The field at point B outside the sphere is ' $E$ '. Now another sphere of radius ' $2 R$ ' having a charge ' $-2 Q$ ' is placed at B. The total field at the point midway betwe...

 A particle ' $A$ ' has charge ' $+q$ ' and a particle ' $B$ ' has charge ' $+4 q$ '. Each has same mass ' $m$ '. When they are allowed to fall from rest through the same potential, the ratio of their speeds will become (particle A to parti...

An electric dipole will have minimum potential energy when it subtends an angle
$$\left[\begin{array}{l} \cos 0^{\circ}=1 \\ \sin 0^{\circ}=0 \end{array}\right]\left[\begin{array}{l} \cos 90^{\circ}=0 \\ \cos \pi=-1 \end{array}\right]$$

Four electric charges $+\mathrm{q},+\mathrm{q},-\mathrm{q}$ and -q are placed in order at the corners of a square of side 2 L. The electric potential at point midway between the two positive charges is

Two point charges +10 q and -4 q are located at $\mathrm{x}=0$ and $\mathrm{x}=\mathrm{L}$ respectively. What is the location of a point on the $x$-axis from the origin, which the net electric field due to these two point charges is zero?( ...

Two point charges $\mathrm{q}_1=6 \mu \mathrm{C}$ and $\mathrm{q}_2=4 \mu \mathrm{C}$ are kept at points $A$ and $B$ in air where $A B=10 \mathrm{~cm}$. What is the increase in potential energy of the system when $\mathrm{q}_2$ is moved tow...

The electric potential at a point on the axis of an electric dipole is proportional to [r = distance between centre of the electric dipole and the point]

If a unit charge is taken from one point to another point over an equipotential surface, then

Two point charges $(A$ and $B)+4 q$ and $-4 q$ are placed along a line separated by a distance I '. Force acting between them is F. If $25 \%$ of charge from point $A$ is transferred to that at point B , the force between the charges now be...

A solid metallic sphere has a charge \(+3 Q\). Concentric with this sphere is a conducting spherical shell having charge \(-\mathrm{Q}\). The radius of the sphere is '\(A\)' and that of the spherical shell is '\(B\)'. \((B > A)\). The elect...

The charges \(2 \mathrm{q},-\mathrm{q},-\mathrm{q}\) are located at the vertices of an equilateral triangle. At the circumcentre of the triangle

When a charge of \(3 ~\mathrm{C}\) is placed in uniform electric field, it experiences a force of \(3000 \mathrm{~N}\). Within this field, potential difference between two points separated by a distance of \(1 \mathrm{~cm}\) is

A conducting sphere of radius \(0.1 \mathrm{~m}\) has uniform charge density \(1.8 \mu \mathrm{C} / \mathrm{m}^2\) on its surface. The electric field in free space at radial distance \(0.2 \mathrm{~m}\) from a point on the surface is ( $$\v...

A uniformly charged semicircular arc of radius '\(r\)' has linear charge density '\(\lambda\)'. The electric field at its centre is ( \(\varepsilon_0=\) permittivity of free space)

The electric field intensity on the surface of a solid charged sphere of radius '\(r\)' and volume charge density '\(\rho\)' is (\(\varepsilon_0=\) permittivity of free space)

If \(\mathrm{E}_{\mathrm{a}}\) and \(\mathrm{E}_{\mathrm{q}}\) represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance '\(r\)' from the centre of the dipole, ...

A charge \(17.7 \times 10^{-4} \mathrm{C}\) is distributed uniformly over a large sheet of area \(200 \mathrm{~m}^2\). The electric field intensity at a distance \(20 \mathrm{~cm}\) from it in air will be $$\left[\varepsilon_0=8.85 \times 1...

Three charges each of value \(+q\) are placed at the corners of an isosceles triangle \(\mathrm{ABC}\) of sides \(\mathrm{AB}\) and \(\mathrm{AC}\) each equal to \(2 \mathrm{a}\). The mid points of \(A B\) and \(A C\) are \(D\) and \(E\) re...

If the magnitude of intensity of electric field at a distance '\(r_1\)' on an axial line and at a distance '\(r_2\)' on an equatorial line due to a given short dipole are equal, then \(r_1: r_2\), is

A charged spherical conductor of radius '\(R\)' is connected momentarily to another uncharged spherical conductor of radius '\(r\)' by means of a thin conducting wire, then the ratio of the surface charge density of the first to the second ...

Which of the following statements is 'WRONG' for the conductors?

In the electric field due to a charge \(Q\), a charge \(q\) moves from point \(A\) to \(B\). The work done is ( \(\varepsilon_0=\) permittivity of vacuum)

The work done in rotating a dipole placed parallel to the electric field through \(180^{\circ}\) is W. So, the work done in rotating it through \(60^{\circ}\) is $$\left(\cos 0^{\circ}=1, \cos 60^{\circ}=\frac{1}{2}, \cos 180^{\circ}=-1\rig...

Two electric dipoles of moment \(\mathrm{P}\) and \(27 \mathrm{P}\) are placed on a line with their centres \(24 \mathrm{~cm}\) apart. Their dipole moments are in opposite direction. At which point the electric field will be zero between th...

Three point charges \(\mathrm{+Q,+2q}\) and \(+\mathrm{q}\) are placed at the vertices of a right angled isosceles triangle. The net electrostatic potential energy of the configuration is zero, if \(Q\) is equal to

Two point charges '\(q 1\)' and '\(q 2\)' are separated by a distance '\(d\)'. What is the increase in potential energy of the system when '\(q 2\)' is moved towards '\(q 1\)' by a distance '\(\mathrm{x}\)' ?
$$(x < d)(\frac{1}{4 \pi \varep...

Select the correct statement from the following.

The bob of a simple pendulum of length '\(L\)' has a mass '\(\mathrm{m}\)' and charge '\(\mathrm{q}\)'. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. ...

Three point charges \(+\mathrm{q},+2 \mathrm{q}\) and \(+\mathrm{Q}\) are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of \(Q\) in terms of \(q\) is

An electron moving with velocity \(1.6 \times 10^7 \mathrm{~m} / \mathrm{s}\) has wavelength of \(0.4 \mathop A\limits^o\). The required accelerating voltage for the electron motion is [charge on electron \(=1.6 \times 10^{-19} \mathrm{C}\)...

Two charges of equal magnitude '\(q\)' are placed in air at a distance '\(2 r\)' apart and third charge '\(-2 \mathrm{q}\)' is placed at mid point. The potential energy of the system is \(\left(\varepsilon_0=\right.\) permittivity of free s...

Two positively charged identical spheres separated by a distance 'd' exert some force (F) on each other when they are kept in air. If both the spheres are immersed in a liquid of dielectric constant 5 , the force experienced by each is (All...

An electron of mass '\(\mathrm{m}\)' and charge '\(\mathrm{q}\)' is accelerated from rest in a uniform electric field of strength '\(E\)'. The velocity acquired by the electron, when it travels a distance '\(\mathrm{L}\)', is

An electric dipole consisting of two opposite charges of \(2 \times 10^{-6} \mathrm{C}\) separated by a distance of \(3 \mathrm{~cm}\) placed in an electric field of \(2 \times 10^5 \mathrm{~N} / \mathrm{C}\) then the maximum torque acting ...

Assume that an electric field \(\mathrm{E}=30 \mathrm{x}^2 \hat{\mathrm{i}}\) exists in space. If '\(\mathrm{V}_0\)' is the potential at the origin and '\(V_A\)' is the potential at \(x=2 \mathrm{~m}\), then the potential difference $$\left...

Three equal charges '\(\mathrm{q}_1\)', '\(^{\prime} \mathrm{q}_2\)' and '\(\mathrm{q}_3\)' are placed on the three corners of a square of side 'a'. If the force between \(\mathrm{q}_1\) and \(\mathrm{q}_2\) is '\(\mathrm{F}_{12}\)' and tha...

If the radius of the spherical gaussian surface is increased then the electric flux due to a point charge enclosed by the surface

Let A, B and C be the three points in a uniform electric field \(\text { ( } \overrightarrow{\mathrm{E}})\) as shown. The electric potential is

The electric field intensity on the surface of a charged solid sphere of radius '\(r\)' and volume charge dentiy '\(\rho\)' is given by (\(\epsilon_0=\) permittivity of free space)

Four electric charges \(+\mathrm{q},+\mathrm{q},-\mathrm{q}\) and \(-\mathrm{q}\) are placed in order at the corners of a square of side \(2 \mathrm{~L}\). The electric potential at point midway between the two positive charges is

Three charges each of \(+1 \mu \mathrm{C}\) are placed at the corners of an equilateral triangle. If the repulsive force between any two charges is \(\mathrm{F}\), then the net force on either charge will be [\(\cos 60^{\circ}=0.5\)]

A charged spherical conductor has radius '\(r\)'. The potential difference between its surface and 3 point at a distance '\(3 r\)' from the centre is '\(v\)' The electric intensity at a distance '\(3 r\)' from the centre of the conductor is

In hydrogen atom an electron revolves around a proton (in nucleus) at a distance 'r' m. the intensity of electric field due to the proton at distance 'r' is \(5 \times 10^{11} \mathrm{NC}^{-1}\), the magnitude of force between the electron ...