Electrostatics

A unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius $R$, having uniform positive charge density $\rho$, as shown in the figure. The initial and final positio...

A point charge $Q$ is placed inside a cavity within a solid isolated conducting sphere. Consider points $A, B$ and $C$ as shown in the figure, where the magnitudes of the electric fields are $E_A, E_B, E_C$, respectively. The points $B$ and...

Consider a fixed uniformly charged insulating sphere with radius $R$ and total charge $+Q$. A point charge $-q$ ( $q \ll Q$ ) with mass $m$ is released from rest at a distance of $3 R$ from the centre of the charged sphere. When the point c...

Which of the following statements are correct?
A. Inside a conductor, the electrostatic field is zero.
B. Electric field at the surface of a charged conductor does not depend on its surface charge density.
C. The interior of a charged condu...

Two identical charged conducting spheres $A$ and $B$ have their centres separated by a certain distance. Charge on each sphere is $q$ and the force of repulsion between them is $F$. A third identical uncharged conducting sphere is brought i...

An electric dipole with dipole moment $5 \times 10^{-6} \mathrm{Cm}$ is aligned with the direction of a uniform electric field of magnitude $4 \times 10^5 \mathrm{~N} / \mathrm{C}$. The dipole is then rotated through an angle of $60^{\circ}...

The value of electric potential at a distance of \(9 \mathrm{~cm}\) from the point charge \(4 \times 10^{-7} \mathrm{C}\) is [Given \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N} \mathrm{~m}^2 \mathrm{C}^{-2}\)] :

A metal cube of side \(5 \mathrm{~cm}\) is charged with \(6 \mu \mathrm{C}\). The surface charge density on the cube is

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:
(Take \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\) SI units)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The potential (V) at any axial point, at \(2 \mathrm{~m}\) distance \((r)\) from the centre of the dipole of dipole moment ve...

If a conducting sphere of radius \(\mathrm{R}\) is charged. Then the electric field at a distance \(\mathrm{r}(\mathrm{r} > \mathrm{R})\) from the centre of the sphere would be, \((\mathrm{V}=\) potential on the surface of the sphere)

A charge \(\mathrm{Q} ~\mu \mathrm{C}\) is placed at the centre of a cube. The flux coming out from any one of its faces will be (in SI unit) :

According to Gauss law of electrostatics, electric flux through a closed surface depends on :

An electric dipole is placed as shown in the figure.

The electric potential (in 102 V) at point P due to the dipole is (\(\in_0\) = permittivity of free space and \(\frac{1}{4 \pi \epsilon_{0}}\) = K) :

If \(\oint_\limits{s} \vec{E} \cdot \overrightarrow{d S}=0\) over a surface, then:

An electric dipole is placed at an angle of \(30^{\circ}\) with an electric field of intensity \(2 \times 10^{5} \mathrm{NC}^{-1}\). It experiences a torque equal to \(4 ~\mathrm{N~m}\). Calculate the magnitude of charge on the dipole, if t...

Six charges +q, \(-\)q, +q, \(-\)q, +q, and \(-\)q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge q0 to the centre of the hexagon from infinity is
(\({\varepsilon _0}\) - permittiv...

Two point charges \(-\)q and +q are placed at a distance of L, as shown in the figure.

The magnitude of electric field intensity at a distance R(R >> L) varies as:

Two hollow conducting spheres of radii R1 and R2 (R1 >> R2) have equal charges. The potential would be

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

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

Two charged spherical conductors of radius R1 and R2 are connected by a wire. Then the ratio of surface charge densities of the spheres (\(\sigma\)1 / \(\sigma\)2) is :

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

Polar molecules are the molecules :

In a certain region of space with volume 0.2 m3, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is :

A short electric dipole has a dipole moment of 16 \(\times\) 10-9 Cm. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of \(60^\circ\) with the d...

A spherical conductor of radius 10 cm has a charge of 3.2 \(\times\) 10-7 C distributed uniformly. That is the magnetude of electric field at a point 15 cm from the centre of the sphere?$$\left( {{1 \over {4\pi {\varepsilon _0}}} = 9 \tim...

Two point charges A and B, having charges +Q and – Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes :

A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre :

Two parallel infinite line charges with linear charge densities +\(\lambda\) C/m and -\(\lambda\) C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?

An electron falls from rest through a vertical
distance h in a uniform and vertically upward
directed electric field E. The direction of electric
field is now reversed, keeping its magnitude the
same. A proton is allowed to fall from rest i...

A toy car with charge q moves on a frictionless
horizontal plane surface under the influence of
a uniform electric field \(\overrightarrow E\)
. Due to the force q\(\overrightarrow E\)
,
its velocity increases from 0 to 6 m s–1 in one
sec...

The diagrams below show regions of equipotentials.

A positive charge is moved from A to B in each diagram.

Suppose the charge of a proton and an electron differ slightly. One of them is \(-\)e, the other is (e + \(\Delta\)e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (musch great...

An electric dipole is placed at an angle of 30o with an electric field intensity 2 \(\times\) 105 N C\(-\)1. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is

Two identical charged spheres suspended from a common point by two massless strings of lengths \(l\), are initially at a distance d(d < < \(l\)) apart because of their mutual repulsion. The charges begin to leak from both the spheres at ...

The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by

If potential (in volts) in a region is expressed as V(x, y, z) = 6xy \(-\) y + 2yz, the electric field (in N/C) at point (1, 1, 0) is

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

In a region, the potential is represented by V(x, y, z) = 6x \(-\) 8xy \(-\) 8y + 6yz,   where \(V\) is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is

An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by 90o is

A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to

A, B and C are three points in a uniform electric field. The electric potential is

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the...

Four point charges \(-\)Q, \(-\)q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of ...

What is the flux through a cube of side \(a\) if a point charge of q is at one of its corner?

Two metallic spheres of radii 1 cm and 3 cm are given charges of \(-\)1 \(\times\) 10\(-\)2 C and 5 \(\times\) 10\(-\)2 C, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is

A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will

Four electric charges +q, +q, \(-\) q and \(-\) q are placed at the corners of a square of side 2L (see figure). The electric potential at point A, midway between the two charges + q and +q, is