Electric Charges and Fields PYQs

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 in contact with sphere A first and then with B and finally removed from both. New force of repulsion between spheres A and B (Radius of A and B are negligible compared to the distance of separation so that for calculating force between them they can be considered as point charges) is best given as :

An electric dipole with dipole moment 5 × 10⁻⁶ Cm is aligned with the direction of a uniform electric field of magnitude 4 × 10⁵ N/C. The dipole is then rotated through an angle of 60° with respect to the electric field. The change in the potential energy of the dipole is :

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 $2\,m$ distance $(r)$ from the centre of the dipole of dipole moment vector $\vec{P}$ of magnitude $4\times10^{-6}\,C\,m$, is $\pm 9\times10^{3}\,V$. (Take: $\frac{1}{4\pi\varepsilon_0}=9\times10^9\;\text{SI units)}$ Reason R: $V = \pm \frac{2P}{4\pi\varepsilon_0 r^2}$ where r is the distance of any axial point situated at 2 m from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:

If $\oint_S \vec{E} \cdot d\vec{S} = 0$ over a surface, then:

The temperature of a gas is -50° C. To what temperature the gas should be heated so that the rms speed is increased by 3 times?

An electric dipole is placed at an angle of $30^\circ$ with an electric field of intensity $2 \times 10^5\, \text{N C}^{-1}$. It experiences a torque equal to $4\, \text{N m}$. Calculate the magnitude of charge on the dipole, if the dipole length is $2\, \text{cm}$.

An electric dipole is placed as shown in the figure. The electric potential (in 10² V) at point P due to the dipole is (ε₀ = permittivity of free space and 1/4π ε₀ = K) :

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

Two point charges −q and +q are placed at a distance L, as shown in the figure. The magnitude of electric field intensity at a distance R (R >> L) varies as:

Polar molecules are the molecules

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

A spherical conductor of radius 10 cm has a charge of $3.2 \times 10^{-7}$ C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere? Take: $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,\text{Nm}^2\text{/C}^2$$

A sphere encloses an electric dipole with charges $\pm 3 \times 10^{-6}\ \text{C}$. What is the total electric flux across the sphere?

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

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 electrostatic force and gravitational force between two hydrogen atoms placed at a distance $d$ apart are zero, then the value of $\Delta e$ is of the order of: (Given: mass of hydrogen atom $m_h = 1.67 \times 10^{-27}\,\text{kg}$)

An electric dipole is placed at an angle of $30^\circ$ with an electric field intensity $2 \times 10^5\ \text{N/C}$. It experiences a torque equal to $4\ \text{N m}$. The charge on the dipole, if the dipole length is $2\ \text{cm}$, 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 respectively 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 the point $(1, 1, 1)$ 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 balls now becomes

Two metallic spheres of radii 1 cm and 3cm are given charges $-1\times10^{-2}\,\text{C}$ and $5\times10^{-2}\,\text{C}$ respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is

A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is

An electric dipole of moment $\vec{P}$ is lying along a uniform electric field. The work done in rotating the dipole by 90° is:

A square surface of side L m is in the plane of the paper. A uniform electric field $\vec{E}$ (V/m) is also in the plane of the paper and is limited only to the lower half of the square surface (see figure). The electric flux in SI units associated with the surface is: