Electrostatics

The plates of a parallel plate capacitor are separated by \(d\). Two slabs of different dielectric constant \(K_1\) and \(K_2\) with thickness \(\frac{3}{8}d\) and \(\frac{d}{2}\), respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If \(K_1 = 1.25\,K_2\), the value of \(K_1\) is :

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 (Radii 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 \(5\times10^{-6}\) Cm is aligned with the direction of a uniform electric field of magnitude \(4\times10^{5}\) N/C. The dipole is then rotated through an angle of \(60^\circ\) with respect to the electric field. The change in the potential energy of the dipole 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 \(\frac{1}{4\pi\epsilon_0}=9\times10^9\) 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 m distance(\(r\)) from the centre of the dipole of dipole moment vector \(\vec{P}\) of magnitude, \(4\times10^{-6}\) C m, is \(\pm9\times10^3\) V.

(Take \(\frac{1}{4\pi\epsilon_0}=9\times10^9\) SI units)

Reason R : \(V=\pm\frac{2P}{4\pi\epsilon_0 r^2}\), 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:

In the following circuit, the equivalent capacitance between terminal \(A\) and terminal \(B\) is :

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then

A. the charge stored in it, increases.

B. the energy stored in it, decreases.

C. its capacitance increases.

D. the ratio of charge to its potential remains the same.

E. the product of charge and voltage increases.

Choose the most appropriate answer from the options given below:

An electric dipole is placed at an angle of \(30^\circ\) with an electric field of intensity \(2\times10^{5}\,\mathrm{N\,C^{-1}}\). It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.

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

The equivalent capacitance of the system shown in the following circuit is :

An electric dipole is placed as shown in the figure. The electric potential (in \(10^2\) V) at point P due to the dipole is (\(\epsilon_0\) = permittivity of free space and \(\frac{1}{4\pi\epsilon_0}=K\)):

Two hollow conducting spheres of radii \(R_1\) and \(R_2\) (\(R_1 >> R_2\)) have equal charges. The potential would be :

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

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 :

A capacitor of capacitance C = 900 pF is charged fully by 100 V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900 pF as shown in figure (b). The electrostatic energy stored by the system (b) is :

The equivalent capacitance of the combination shown in the figure is :

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

A parallel plate capacitor has a uniform electric field '\(\vec{E}\)' in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is : (\(\varepsilon_0\) = permittivity of free space)

Polar molecules are the molecules :

Two charged spherical conductors of radius \(R_1\) and \(R_2\) are connected by a wire. Then the ratio of surface charge densities of the spheres (\(\sigma_1/\sigma_2\)) is :

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

A spherical conductor of radius 10 cm has a charge of \(3.2\times10^{-7}\) C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere ?

\(\left(\frac{1}{4\pi\epsilon_0} = 9\times10^9\ \text{N m}^2/\text{C}^2\right)\)

In a certain region of space with volume 0.2 m\(^3\), the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is :

The capacitance of a parallel plate capacitor with air as medium is 6 \(\mu\)F. With the introduction of a dielectric medium, the capacitance becomes 30 \(\mu\)F. The permittivity of the medium is :

(\(\epsilon_0 = 8.85\times10^{-12}\) C\(^2\) N\(^{-1}\) m\(^{-2}\))

A short electric dipole has a dipole moment of \(16\times10^{-9}\) C m. 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 dipole axis is :

\(\left(\frac{1}{4\pi\epsilon_0} = 9\times10^9\ \text{N m}^2/\text{C}^2\right)\)

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 ?

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 :

The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is

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 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

A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system :

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 (much greater than atomic size) apart is zero, then \(\Delta e\) is of the order of [Given mass of hydrogen \(m_h = 1.67\times10^{-27}\) kg]

A capacitor of \(2\ \mu F\) is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated 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 a constant rate. As a result, the spheres approach each other with a velocity \(v\). Then \(v\) varies as a function of the distance \(x\) between the spheres, as :

An electric dipole is placed at an angle of 30° with an electric field intensity \(2\times10^5\) N/C. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is

A parallel-plate capacitor of area \(A\), plate separation \(d\) and capacitance \(C\) is filled with four dielectric materials having dielectric constants \(k_1,k_2,k_3\) and \(k_4\) as shown in the figure below. If a single dielectric material is to be used to have the same capacitance \(C\) in this capacitor, then its dielectric constant \(k\) is given by