An electric charge $10^{-3} \mu \mathrm{C}$ is placed at the origin of $x y$-plane. The potential difference between point $A$ and $B$ located at $(\sqrt{2} \mathrm{~m}, \sqrt{2} \mathrm{~m})$ and $(2 \mathrm{~m}, 0 \mathrm{~m})$ respectively is

If two particles $A$ and $B$ of charges $1.6 \times 10^{-19} \mathrm{C}$ and $3.2 \times 10^{-19} \mathrm{C}$ respectively are separated by a distance of 3 cm in air, then the magnitude of electrostatic force on particle $A$ due to particle $B$ is

If four charges $+12 \mathrm{nC},-20 \mathrm{nC},+32 \mathrm{nC}$ and -15 nC are arranged at the four vertices of a square of side $\sqrt{2} \mathrm{~m}$, then the net electric potential at the centre of the square due to these four charges is

The force between two conducting spheres of same radius having charges $+8 \mu \mathrm{C}$ and $-4 \mu \mathrm{C}$ separated by some distance in air is $F$. If the spheres are connected by a conducting wire and after some time the wire is removed, then the magnitude of the force between the two conducting spheres is

In space the electric potential varies as $V=20|\mathbf{r}|$ volt. where $\mathbf{r}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}$ is the position vector. Then, electric field in $\left(\mathrm{NC}^{-1}\right)$ at the point $(4 \mathrm{~m}, 3 \mathrm{~m},-5 \mathrm{~m})$ is

The sum of two point positive charges separated by a distance of 1.5 m in air is $25 \mu \mathrm{C}$. If the electrostatic force between the two charges is 0.6 N , then the difference between the two charges is

A solid of mass 1 kg has $6 \times 10^{24}$ atoms. If one electron is removed from every one atom of $0.005 \%$ of the atoms, then the charge gained by the solid is

If the energy stored in a spherical conductor having a charge of $12 \mu \mathrm{C}$ is 6 J , then the radius of the spherical conductor is

Two charged conducting spheres of radii 5 cm and 10 cm have equal surface charge densities. If the electric field on the surface of the smaller sphere is $E$, then the electric field on the surface of the larger sphere is

As shown in the figure, if the values of the electric potential at three points $A, B$ and $C$ in a uniform electric field (E) are $V_A, V_B$ and $V_C$ respectively, then

As shown in the figure, the work done to move the charge ' $Q$ ' from point $C$ to point $D$ along the semicircle CRD is

In a region, the electric field is given by $\mathbf{E}=(3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}) \mathrm{NC}^{-1}$. The electric flux through a surface of area $3 \mathrm{~m}^2$ in $y z$-plane is (in SI units)

The velocity acquired by an electron at rest when subjected to a uniform electric field of potential difference 180 V is

(Mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ and charge of electron $=1.6 \times 10^{-19} \mathrm{C}$ )

Three particles of each charge $q$ are placed at the vertices of an equilateral triangle of side $L$. The work to be done to decrease the side of the triangle to $\frac{L}{2}$ is

If 27 charged water droplets, each of radius $10^{-3} \mathrm{~m}$ and charge $10^{-12} \mathrm{C}$ coalesce to form a single big spherical drop, then the potential of the big drop is

The force between two point charges kept with a separation of 9 cm in air is 98 N . If a dielectric slab of constant 4, thickness 6 cm and another dielectric slab of constant 9 , thickness 3 cm are introduced between the two charges, then the new force becomes

Three point charges shown in the figure lie along a straight line. The energy required to exchange the position of central charge with one of the negative charges is

The magnitude of an electric field which can just suspend a deuteron of mass $3.2 \times 10^{-27} \mathrm{~kg}$ freely in ari is

A large number of positive charges each of magnitude $q$ are placed along the $X$-axis at the origin and at every 1 cm distance in both the directions. The electric flux through a spherical surface of radius 2.5 cm centred at the origin is

The electric field in a region of space is given as $\mathbf{E}=\left(5 \mathrm{NC}^{-1}\right) x \hat{i}$. Consider point $A$ on the $Y$-axis at $y=5 \mathrm{~m}$ and point $B$ on the $X$-axis at $x=2 \mathrm{~m}$. If the potentials at points $A$ and $B$ are $V_A$ and $V_B$ respectively, then $\left(V_B-V_A\right)$ is

A solid sphere of radius $R$ carries a positive charge $Q$ distributed uniformly throughout its volume. A very thin hole is drilled through it's centre. A particle of mass $m$ and charge $-$q performs simple harmonic motion about the centre of the sphere in this hole. The frequency of oscillation is

Assertion (A) In a region of constant potential, the electric field is zero and there can be no charge inside the region.

Reason (R) According to Gauss law, charge inside the region should be zero if electric field is zero.

Statement (A) Inside a charged hollow metal sphere, $E=0, V \neq 0$, (where, $E=$ electric field, $V=$ electric potential).

Statement (B) The work done in moving a positive charge on an equipotential surface is zero.

Statement (C) When two like charges are brought closer, their mutual electrostatic potential energy will increase.

Electrostatic force between two identical charges placed in vacuum at distance of $r$ is F. A slab of width $\frac{r}{5}$ and dielectric constant 9 is inserted between these two charges, then the force between the charges is

An electric dipole with dipole moment $5 \times 10^{-7} \mathrm{C}-\mathrm{m}$ is in the electric field of $2 \times 10^4 \mathrm{NC}^{-1}$ at an angle of $60^{\circ}$ with the direction of the electric field. The torque acting on the dipole is

Two positive point charges of $10 \mu \mathrm{C}$ and $12 \mu \mathrm{C}$ are placed 10 cm apart in air. The work done to bring them 6 cm closer is

Two charges $10 ~\mu \mathrm{C}$ and $-10 ~\mu \mathrm{C}$ are placed at points $A$ and $B$ separated by a distance of $10 \mathrm{~cm}$. Find the electric field at a point $P$ on the perpendicular bisector of $A B$, at a distance of $12 \mathrm{~cm}$ from its mid-point.

When a number of charged liquid drops coalesce, which of the following quantity does not change?

What is the angle between maximum value of potential gradient and equipotential surface?

What is the electric flux for Gaussian surface $A$ that encloses the charged particles in free space? [Given, $q_1=-14 \mathrm{~nC}, q_2=78.85 \mathrm{~nC}, \left.q_3=-56 \mathrm{~nC}\right]$

Two charges 8 $\mu$C each are placed at the corners A and B of an equilateral triangle of side 0.2 m in air. The electric potential at the third corner C is

Gauss's law helps in

Charge on the outer sphere is $q$ and the inner sphere is grounded. The charge on the inner sphere is $q^{\prime}$, for $\left(r_2 > r_1\right)$. Then,

Which statement(s) among the following are incorrect?

(i) A negative test charge experiences a force opposite to the direction of the field.

(ii) The tangent drawn to a line of force represents the direction of electric field.

(iii) The electric field lines never intersect.

(iv) The electric field lines form a closed loop.