Electric Charges and Fields PYQs

Five capacitors of capacitances C₁ = C₂ = C₃ = C₄ = 10 μF and C₅ = 2.5 μF are connected as shown, along with a battery of 50 V. The equivalent capacitance and the charges on each capacitor respectively are:

Consider two uncharged capacitors of equal capacitance 200 pF. One of them is charged by a 100 V supply and disconnected. Now this capacitor is connected to the uncharged capacitor. The amount of electrostatic energy lost in the process is:

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 conductor can have no excess charge in the static situation. D. At the surface of a charged conductor, the electrostatic field must be normal to the surface at every point. E. The electrostatic potential is zero everywhere inside a charged conductor. Choose the correct answer from the options given below:

The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant $K_1$ and $K_2$ with thicknesses 3/8(d) and 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 (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 :

In the following circuit, the equivalent capacitance between terminal A and terminal B 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:

A thin spherical shell is charged by some source. The potential difference between two points C and P (in V) shown in the figure is: (Take 1/(4πϵ₀) = 9 × 10⁹ SI units)

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:

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

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 ac source is connected to a capacitor C. Due to decrease in its operating frequency :

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) :

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 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 a 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:

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 $\left(\frac{\sigma_1}{\sigma_2}\right)$ is:

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)

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: $$\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,\text{Nm}^2\text{/C}^2$$

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 μF. With the introduction of a dielectric medium, the capacitance becomes 30 μF. The permittivity of the medium is : (ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²)

A short electric dipole has a dipole moment of 16 × 10⁻⁹ 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° with the dipole axis is: [1/(4π ε₀) = 9 × 10⁹ N m²/C²]

Two metal spheres, one of radius $R$ and the other of radius $2R$ respectively have the same surface charge density $\sigma$. They are brought in contact and separated. What will be the new surface charge densities on them?

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

Two identical capacitors $C_1$ and $C_2$ of equal capacitance are connected as shown in the circuit. Terminals $a$ and $b$ of the key $k$ are connected to charge capacitor $C_1$ using a battery of emf $V$. Now disconnecting $a$ and $b$, the terminals $b$ and $c$ are connected. Due to this, what will be the percentage loss of energy?

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:

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

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 $m_h = 1.67 \times 10^{-27}\,\text{kg}$)

The diagrams below show regions of equipotentials. A positive charge is moved from $A$ to $B$ in each diagram. Identify the correct statement regarding the work required.

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 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 $C$, then its dielectric constant $k$ is 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 the point (1, 1, 0) is:

Two thin dielectric slabs of dielectric constants $K_1$ and $K_2$ ($K_1 < K_2$) are inserted between the plates of a parallel plate capacitor as shown in the figure. The variation of electric field 'E' between the plates with distance 'd' as measured from plate $P$ is correctly shown by:

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

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

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 potential V at any point (x, y, z), all in meters in space is given by V = 4x² volt. The electric field at the point (1, 0, 2) in volt/meter is:

Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC and AC equal to 2a. D and E are the mid points of BC and CA. The work done in taking a charge Q from D to E is:

Two parallel metal plates having charges +Q and -Q face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will

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

Three capacitors each of capacitance $C$ and breakdown voltage $V$ are joined in series. The equivalent capacitance and breakdown voltage of the combination will be:

The electric potential at a point $(x,y,z)$ is given by: $$V=-x^2y-xz^3+4$$

Three concentric spherical shells have radii $a$, $b$, and $c$ $(a<b<c)$ and have surface charge densities $\sigma$, $-\sigma$, and $\sigma$ respectively. If $V_A$, $V_B$, and $V_C$ denote the potentials of the shells, then for $c=a+b$, we have:

The energy required to charge a parallel plate condenser of plate separation d and plate area of cross-section A such that the uniform electric field between the plates is E, 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

The electric potential at a point in free space due to a charge Q coulomb is Q × 10¹¹ volts. The electric field at that point is

A solid sphere of radius a having charge q is placed inside a spherical shell of inner radius r and outer radius R. Find the potential at distance x, where r < x < R.

A conducting cone is given charge q. How do the charge density and electric potential vary at different points of the cone?

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 parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates:

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:

A network of four capacitors of capacitances $C_1=C$, $C_2=2C$, $C_3=3C$ and $C_4=4C$ are connected to a battery as shown. The ratio of charges on $C_2$ and $C_4$ is:

A point charge $+q$ is placed at the origin $O$. Work done in taking another point charge $-Q$ from point $A(0,a)$ to point $B(a,0)$ along the straight path $AB$ is:

Two charges $q_1$ and $q_2$ are placed $30\,\text{cm}$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40\,\text{cm}$ from $C$ to $D$. The change in the potential energy of the system is where $k$ is: