Electrostatics

Expression for an electric field is given by \(\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{m}}\). The electric flux through the cube of side \(20 \mathrm{~cm}\) when placed in electric field (as shown in the fig...

Which of the following correctly represents the variation of electric potential \((\mathrm{V})\) of a charged spherical conductor of radius \((\mathrm{R})\) with radial distance \((\mathrm{r})\) from the center?

Considering a group of positive charges, which of the following statements is correct ?

Two isolated metallic solid spheres of radii \(\mathrm{R}\) and \(2 \mathrm{R}\) are charged such that both have same charge density \(\sigma\). The spheres are then connected by a thin conducting wire. If the new charge density of the bigg...

Electric field in a certain region is given by \(\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\right) \text {. The } \mathrm{SI} \text { unit of } \mathrm{A} \text { and } \mathrm{B}\) a...

As shown in figure, a cuboid lies in a region with electric field $E=2 x^{2} \hat{i}-4 y \hat{j}+6 \hat{k} \mathrm{~N} / \mathrm{C}$. The magnitude of charge within the cuboid is $n \in_{0} C$.

The value of $n$ is _________ (if dimension o...

As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $\mathrm{Q}$ in three different regions $\mathrm{I}, \mathrm{II}$ an...

A point charge \(q_1=4q_0\) is placed at origin. Another point charge \(q_2=-q_0\) is placed at \(x=12\) cm. Charge of proton is \(q_0\). The proton is placed on \(x\) axis so that the electrostatic force on the proton is zero. In this situ...

In a cuboid of dimension \(2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}\), a charge \(q\) is placed at the center of the surface '\(\mathrm{S}\)' having area of \(4 \mathrm{~L}^{2}\). The flux through the opposite surface to '$$\mat...

For a charged spherical ball, electrostatic potential inside the ball varies with \(r\) as \(\mathrm{V}=2ar^2+b\).
Here, \(a\) and \(b\) are constant and r is the distance from the center. The volume charge density inside the ball is $$-\la...

A point charge \(2\times10^{-2}~\mathrm{C}\) is moved from P to S in a uniform electric field of \(30~\mathrm{NC^{-1}}\) directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done b...

A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle...

A point charge of 10 \(\mu\)C is placed at the origin. At what location on the X-axis should a point charge of 40 \(\mu\)C be placed so that the net electric field is zero at \(x=2\)cm on the X-axis?

A stream of a positively charged particles having \({q \over m} = 2 \times {10^{11}}{C \over {kg}}\) and velocity \({\overrightarrow v _0} = 3 \times {10^7}\widehat i\,m/s\) is deflected by an electric field \(1.8\widehat j\) kV/m. The elec...

If two charges q\(_1\) and q\(_2\) are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

The electric potential at the centre of two concentric half rings of radii R\(_1\) and R\(_2\), having same linear charge density \(\lambda\) is :

Two equal positive point charges are separated by a distance \(2 a\). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge $$\mat...

Let \(\sigma\) be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region \(E_{I}, E_{I I}\) and \(E_{I I I}\) are:

A cubical volume is bounded by the surfaces \(\mathrm{x}=0, x=\mathrm{a}, y=0, y=\mathrm{a}, \mathrm{z}=0, z=\mathrm{a}\). The electric field in the region is given by \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} x \hat{i}\). Where $$\mathr...

The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as :

A thin infinite sheet charge and an infinite line charge of respective charge densities \(+\sigma\) and \(+\lambda\) are placed parallel at \(5 \mathrm{~m}\) distance from each other. Points 'P' and 'Q' are at \(\frac{3}{\pi}\) m and $$\fra...

Two charges each of magnitude \(0.01 ~\mathrm{C}\) and separated by a distance of \(0.4 \mathrm{~mm}\) constitute an electric dipole. If the dipole is placed in an uniform electric field '\(\vec{E}\)' of 10 dyne/C making \(30^{\circ}\) angl...

Three point charges \(\mathrm{q},-2 \mathrm{q}\) and \(2 \mathrm{q}\) are placed on $x$-axis at a distance \(x=0, x=\frac{3}{4} R\) and \(x=R\) respectively from origin as shown. If \(\mathrm{q}=2 \times 10^{-6} \mathrm{C}\) and $$\mathrm{R...

A \(10 ~\mu \mathrm{C}\) charge is divided into two parts and placed at \(1 \mathrm{~cm}\) distance so that the repulsive force between them is maximum. The charges of the two parts are:

64 identical drops each charged upto potential of \(10 ~\mathrm{mV}\) are combined to form a bigger drop. The potential of the bigger drop will be __________ \(\mathrm{mV}\).

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : If an electric dipole of dipole moment \(30 \times 10^{-5} ~\mathrm{C} ~\mathrm{m}\) is enclosed by a closed surface, the net...

As shown in the figure, a configuration of two equal point charges \(\left(q_{0}=+2 \mu \mathrm{C}\right)\) is placed on an inclined plane. Mass of each point charge is \(20 \mathrm{~g}\). Assume that there is no friction between charge and...

Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [a < b < c] have surface charge densities \(\sigma,-\sigma\) and \(\sigma\) respectively. The shells X and Z are at same potential. If the radii of X & ...

An electron revolves around an infinite cylindrical wire having uniform linear charge density \(2 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}\) in circular path under the influence of attractive electrostatic field as shown in the figure. The...

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

Eight similar drops of mercury are maintained at 12 V each. All these spherical drops combine into a single big drop. The potential energy of bigger drop will be ____________ E. Where E is the potential energy of a single smaller drop.

A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 \(\times\) 105 NC\(-\)1. If the charge on the particle is 40 \(\mu\)C and the initial velocity is 200 ms\(-\)1, how much distance...

If the electric potential at any point (x, y, z) m in space is given by V = 3x2 volt. The electric field at the point (1, 0, 3) m will be :

Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-point on the perpendicular bisector. The value of x at which charge q will experience the maximum Coulomb's force is :

Given below are two statements.
Statement I : Electric potential is constant within and at the surface of each conductor.
Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at eve...

A spherically symmetric charge distribution is considered with charge density varying as
$$\rho(r)= \begin{cases}\rho_{0}\left(\frac{3}{4}-\frac{r}{R}\right) & \text { for } r \leq R \\ \text { zero } & \text { for } r>R\end{cases}$$
Where,...

Two identical metallic spheres \(\mathrm{A}\) and \(\mathrm{B}\) when placed at certain distance in air repel each other with a force of \(\mathrm{F}\). Another identical uncharged sphere \(\mathrm{C}\) is first placed in contact with $$\ma...

The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the corner D of the square, is :

Given below are two statements :
Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.
Statement II : An electric dipole is placed in ...

Two point charges A and B of magnitude +8 \(\times\) 10\(-\)6 C and \(-\)8 \(\times\) 10\(-\)6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 \(\times\) 104 NC\(-\)1. The...

Two electric dipoles of dipole moments \(1.2 \times 10^{-30} \,\mathrm{Cm}\) and \(2.4 \times 10^{-30} \,\mathrm{Cm}\) are placed in two different uniform electric fields of strengths \(5 \times 10^{4} \,\mathrm{NC}^{-1}\) and $$15 \times 1...

A uniform electric field \(\mathrm{E}=(8 \mathrm{~m} / \mathrm{e}) \,\mathrm{V} / \mathrm{m}\) is created between two parallel plates of length \(1 \mathrm{~m}\) as shown in figure, (where \(\mathrm{m}=\) mass of electron and e = charge of ...

Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1m.
The ratio of net force on a charged ball to the force betwe...

If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :

A long cylindrical volume contains a uniformly distributed charge of density \(\rho \,\mathrm{Cm}^{-3}\). The electric field inside the cylindrical volume at a distance \(x=\frac{2 \varepsilon_{0}}{\rho} \mathrm{m}\) from its axis is ______...

Two identical positive charges \(Q\) each are fixed at a distance of '2a' apart from each other. Another point charge \(q_{0}\) with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining t...

A charge of \(4 \,\mu \mathrm{C}\) is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be :

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).
Assertion (A) : Non-polar materials do not have any permanent dipole moment.
Reason (R) : When a non-polar material is placed in an electric ...

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 \(\mu\)C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :

Three point charges of magnitude \(5 \mu \mathrm{C}, 0.16 \mu \mathrm{C}\) and \(0.3 \mu \mathrm{C}\) are located at the vertices \(A, B, C\) of a right angled triangle whose sides are \(A B=3 \mathrm{~cm}, B C=3 \sqrt{2} \mathrm{~cm}\) and...