Electrostatics — CBSE Class 12 board PYQs

Assertion (A): Equal amounts of positive and negative charges are distributed uniformly on two halves of a thin circular ring as shown in the figure. The resultant electric field at the centre O of the ring is along OC. Reason (R): It is so because the net potential at O is not z …

The magnitude of the electric field due to a point charge object at a distance of 4.0 m is 9 N/C. From the same charged object the electric field of magnitude 16 N/C will be at a distance of

A point P lies at a distance $x$ from the midpoint of an electric dipole on its axis. The electric potential at point P is proportional to

Assertion (A): Work done in moving a charge around a closed path in an electric field is always zero. Reason (R): Electrostatic force is a conservative force.

If the net electric flux through a closed surface is zero, then we can infer

An electric dipole consisting of charges $+q$ and $-q$ separated by a distance $L$ is in stable equilibrium in a uniform electric field $\vec{E}$. The electrostatic potential energy of the dipole is

Draw the pattern of electric field lines when a point charge $+q$ is kept near an uncharged conducting plate.

Draw a plot showing variation of electric field with distance from the centre of a solid conducting sphere of radius $R$, having a charge $+Q$ on its surface.

Does the charge given to a metallic sphere depend on whether it is hollow or solid? Give reason for your answer.

A point charge $+Q$ is placed at point O as shown in the figure. Is the potential difference $V_A-V_B$ positive, negative or zero?

How does the electric flux due to a point charge enclosed by a spherical Gaussian surface get affected when its radius is increased?

What is the amount of work done in moving a point charge $Q$ around a circular arc of radius $r$ at the centre of which another point charge $q$ is located?

What is the electric flux through a cube of side 1 cm which encloses an electric dipole?

Why do the electric field lines never cross each other?

Two charges of magnitudes $+4Q$ and $-Q$ are located at points $(a,0)$ and $(-3a,0)$ respectively. What is the electric flux due to these charges through a sphere of radius $2a$ with its centre at the origin?

Why should electrostatic field be zero inside a conductor?

Define electric dipole moment. Write its S.I. unit.

A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. What is the potential at the centre of the sphere?

The figure shows three point charges $+2q$, $-q$ and $+3q$. Two charges $+2q$ and $-q$ are enclosed within a surface $S$. What is the electric flux due to this configuration through the surface $S$?

In which orientation, a dipole placed in a uniform electric field is in
(i) stable,
(ii) unstable equilibrium?

What is the work done in moving a test charge $q$ through a distance of 1 cm along the equatorial axis of an electric dipole?

Draw an equipotential surface for a system consisting of two charges $Q$, $-Q$ separated by a distance $r$ in air.

Define the term electric dipole moment. Is it a scalar or a vector quantity?

An electric dipole of dipole moment $20\times 10^{-6}\text{C m}$ is enclosed by a closed surface. What is the net flux coming out of the surface?

An electrostatic field line cannot be discontinuous. Why?

How does the Coulomb force between two point charges depend upon the dielectric constant of the intervening medium?

Two electric field lines never cross each other. Why?

Two point charges $q_A=+3\mu \text{C}$ and $q_B=-3\mu \text{C}$ are located 20 cm apart in vacuum.
(i) Find the electric field at the mid-point of the line AB joining the two charges.
(ii) If a negative test charge of magnitude $1.5\times 10^{-9}\text{C}$ is placed at th …

Write the S.I. unit of
(i) electric field intensity and
(ii) electric dipole moment.

Four point charges of $1\mu \text{C}$, $-2\mu \text{C}$, $1\mu \text{C}$ and $-2\mu \text{C}$ are placed at the corners A, B, C and D respectively of a square of side 30 cm. Find the net force acting on a charge of $4\mu \text{C}$ placed at the centre of the square.

Three point charges $1\text{pC}$ each are kept at the vertices of an equilateral triangle of side 10 cm. Find the net electric field at the centroid of the triangle.

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a wire. Find the ratio of the electric fields at their surfaces.

(a) Draw the equipotential surfaces due to an electric dipole.
(b) Derive an expression for the electric field due to a dipole of dipole moment $\vec{p}$ at a point on its perpendicular bisector.

Four point charges $Q$, $q$, $Q$ and $q$ are placed at the corners of a square of side $a$ as shown in the figure. Find the:
(a) resultant electric force on a charge $Q$, and
(b) potential energy of this system.

Three point charges $q$, $-4q$ and $2q$ are placed at the vertices of an equilateral triangle ABC of side $\ell$ as shown in the figure. Obtain
(a) the expression for the magnitude of the resultant electric force acting on the charge $q$, and
(b) the amount of work done to separa …

(a) Write two properties by which electric potential is related to the electric field.
(b) Two point charges $q_1$ and $q_2$, separated by a distance of $r_{12}$ are kept in an external electric field. Derive an expression for the potential energy of the system of two charges in …

State Gauss's law in electrostatics. Derive an expression for the electric field due to an infinitely long straight uniformly charged wire.

(i) Derive the expression for the electric potential due to an electric dipole at a point on its axial line.
(ii) Depict the equipotential surfaces due to an electric dipole.

Find the electric field intensity due to a uniformly charged spherical shell at a point
(i) outside the shell and
(ii) inside the shell. Plot the graph of electric field with distance from the centre of the shell.

A charge is distributed uniformly over a ring of radius $a$. Obtain an expression for the electric intensity $E$ at a point on the axis of the ring. Hence show that for points at large distances from the ring, it behaves like a point charge.

Draw a plot showing the variation of
(i) electric field ($E$) and
(ii) electric potential ($V$) with distance $r$ due to a point charge $Q$.

A thin straight infinitely long conducting wire having charge density $\lambda$ is enclosed by a cylindrical surface of radius $r$ and length $\ell$, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.

Plot a graph showing the variation of Coulomb force ($F$) versus $\left(\frac{1}{r^2}\right)$, where $r$ is the distance between the two charges of each pair of charges $(1\mu \text{C},2\mu \text{C})$ and $(2\mu \text{C},-3\mu \text{C})$. Interpret the graphs obtained.

(a) Depict the equipotential surfaces for a system of two identical positive point charges placed a distance $d$ apart.
(b) Deduce the expression for the potential energy of a system of two point charges $q_1$ and $q_2$ brought from infinity to the points ${\vec{r}}_1$ and …

Draw equipotential surfaces corresponding to a field that uniformly increases in magnitude but remains constant along Z-direction. How are these surfaces different from that of a constant electric field along Z-direction?

Define electric flux. Write its S.I. unit. A charge $q$ is enclosed by a spherical surface of radius $r$. If the radius is reduced to half, how would the electric flux through the surface change?

Use Gauss's law to derive the expression for the electric field between two uniformly charged large parallel sheets with surface charge densities $\sigma$ and $-\sigma$ respectively.

(a) A charge $+Q$ is placed on a large spherical conducting shell of radius $R$. Another small conducting sphere of radius $r$ carrying charge $q$ is introduced inside the large shell and is placed at its centre. Find the potential difference between two points, one lying on the …

State Gauss's law in electrostatics. Using this law derive an expression for the electric field due to a uniformly charged infinite plane sheet.

Derive an expression for the torque acting on an electric dipole, which is held in a uniform electric field, when the axis of the dipole makes an angle $\theta$ with the electric field.

The electric field $E$ due to a point charge at any point near it is defined as $E=\underset{q\to 0}{\lim }\frac{F}{q}$, where $q$ is the test charge and $F$ is the force acting on it. What is the physical significance of $\underset{q\to 0}{\lim }$ in this expression? Draw the elect …

Define electric flux. Write its S.I. units. A spherical rubber balloon carries a charge that is uniformly distributed over its surface. As the balloon is blown up and increases in size, how does the total electric flux coming out of the surface change? Give reason.

Deduce an expression for the electric potential due to an electric dipole at any point on its axis. Mention one contrasting feature of electric potential of a dipole at a point as compared to that due to a single charge.

The electric field and electric potential at any point due to a point charge kept in air are $20{\text{N C}}^{-1}$ and $10{\text{J C}}^{-1}$ respectively. Compute the magnitude of this charge.

Using Gauss's theorem, show mathematically that for any point outside the shell, the field due to a uniformly charged thin spherical shell is the same as if the entire charge of the shell is concentrated at the centre. Why do you expect the electric field inside the shell to be z …

What is electric flux? Write its S.I. units. Using Gauss's theorem, deduce an expression for the electric field at a point due to a uniformly charged infinite plane sheet.

Define 'electric line of force' and give its two important properties.

Three point charges of $+2\mu \text{C}$, $-3\mu \text{C}$ and $-3\mu \text{C}$ are kept at the vertices A, B and C respectively of an equilateral triangle of side 20 cm as shown in the figure. What should be the sign and magnitude of the charge to be placed at the mid-point (M …

An electric dipole is held in a uniform electric field.
(i) Using a suitable diagram, show that it does not undergo any translatory motion, and
(ii) derive an expression for the torque acting on it and specify its direction.

Define electric field intensity. Write its S.I. unit. Write the magnitude and direction of electric field intensity due to an electric dipole of length $2a$ at the mid-point of the line joining the two charges.

A charge $q$ is placed at the centre of the line joining two equal charges $Q$. Show that the system of three charges will be in equilibrium if $q=-\frac{Q}{4}$.

Two fixed point charges $+4e$ and $+e$ units are separated by a distance $a$. Where should the third point charge be placed for it to be in equilibrium?

State Gauss's theorem. Apply this theorem to obtain the expression for the electric field intensity at a point due to an infinitely long, thin, uniformly charged straight wire.

An electric dipole of length 8 cm, when placed with its axis making an angle of $60^{\circ }$ with a uniform electric field, experiences a torque of $8\sqrt{3}\text{N m}$. Calculate the
(i) magnitude of the electric field,
(ii) potential energy of the dipole, if the dipole has cha …

An electric dipole of length 4 cm, when placed with its axis making an angle of $30^{\circ }$ with a uniform electric field, experiences a torque of $4\text{N m}$. Calculate the
(i) magnitude of the electric field,
(ii) potential energy of the dipole, if the dipole has charges of …

An electric dipole of length 4 cm, when placed with its axis making an angle of $60^{\circ }$ with a uniform electric field, experiences a torque of $4\sqrt{3}\text{N m}$. Calculate the
(i) magnitude of the electric field,
(ii) potential energy of the dipole, if the dipole has cha …

State Gauss's theorem in electrostatics. Using this theorem, derive an expression for the electric field intensity due to an infinite plane sheet of charge of charge density $\sigma {\text{C m}}^{-2}$.

Two similarly and equally charged identical metal spheres A and B repel each other with a force of $2\times 10^{-5}\text{N}$. A third identical uncharged sphere C is touched with A and then placed at the mid-point between A and B. Calculate the net electric force on C.

Give the principle of working of a Van de Graaff generator. With the help of a labelled diagram, describe its construction and working. How is the leakage of charge minimized from the generator?

(a)(i) Draw equipotential surfaces for an electric dipole. (ii) Two point charges $q_1$ and $q_2$ are located at ${\vec{r}}_1$ and ${\vec{r}}_2$ respectively in an external electric field $\vec{E}$. Obtain an expression for the potential energy of the system. (iii) The dipole moment …

(b)(i) A thin spherical shell of radius $R$ has a uniform surface charge density $\sigma$. Using Gauss's law, deduce an expression for the electric field (i) outside and (ii) inside the shell. (ii) Two long straight thin wires AB and CD have linear charge densities …

(a)(i) Use Gauss's law to obtain an expression for the electric field due to an infinitely long thin straight wire with uniform linear charge density $\lambda$. (ii) An infinitely long positively charged straight wire has a linear charge density $\lambda$. An electron is revolvin …

(b)(i) Consider two identical point charges located at points $(0,0)$ and $(a,0)$. (1) Is there a point on the line joining them at which the electric field is zero? (2) Is there a point on the line joining them at which the electric potential is zero? Justify. (ii) State the si …

(a) Using Gauss law, derive the expression for the electric field due to a spherical shell of uniform charge distribution $\sigma$ and radius $R$ at a point lying at a distance $x$ from the centre of the shell, such that (i) $0<x<R$, and (ii) $x>R$. (b) An electric field is …

(a) Find the expression for the potential energy of a system of two point charges $q_1$ and $q_2$ located at ${\vec{r}}_1$ and ${\vec{r}}_2$ respectively in an external electric field $\vec{E}$.
(b) Draw equipotential surfaces due to an isolated point charge $(-q)$ and depict the ele …

(a) Derive an expression for the electric field at any point on the equatorial line of an electric dipole.
(b) Two identical point charges, $q$ each, are kept 2 m apart in air. A third point charge $Q$ of unknown magnitude and sign is placed on the line joining the charges such t …

(a) Define electric flux. Is it a scalar or a vector quantity? A point charge $q$ is at a distance of $\frac{d}{2}$ directly above the centre of a square of side $d$, as shown in the figure. Use Gauss's law to obtain the expression for the electric flux through the square.
(b) I …

(a) Use Gauss's law to derive the expression for the electric field $\vec{E}$ due to a straight uniformly charged infinite line of charge density $\lambda {\text{C m}}^{-1}$.
(b) Draw a graph to show the variation of $E$ with perpendicular distance $r$ from the line of charge.
(c) …

(a) Explain why, for any charge configuration, the equipotential surface through a point is normal to the electric field at that point. Draw a sketch of equipotential surfaces due to a single charge $(-q)$, depicting the electric field lines due to the charge.
(b) Obtain an expre …

(a) An electric dipole of dipole moment $\vec{p}$ consists of point charges $+q$ and $-q$ separated by a distance $2a$ apart. Deduce the expression for the electric field $\vec{E}$ due to the dipole at a distance $x$ from the centre of the dipole on its axial line in terms of the …

(a) Explain, using suitable diagrams, the difference in the behaviour of a (i) conductor and (ii) dielectric in the presence of an external electric field. Define the terms polarization of a dielectric and write its relation with susceptibility. (b) A thin metallic spherical shel …

Draw a labelled diagram of a Van de Graaff generator. State its working principle to show how by introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitati …

(a) Deduce the expression for the torque acting on a dipole of dipole moment $\vec{p}$ in the presence of a uniform electric field $\vec{E}$. (b) Consider two hollow concentric spheres, $S_1$ and $S_2$, enclosing charges $2Q$ and $4Q$ respectively as shown in the figure. (i) Find …

(a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.
(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to th …

Using Gauss's law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius $R$ at a point
(i) outside and
(ii) inside the shell. Plot a graph showing the variation of electric field as a function of $r>R$ and $r<R$ ($r$ bein …

Explain the principle of a device that can build up high voltages of the order of a few million volts. Draw a schematic diagram and explain the working of this device. Is there any restriction on the upper limit of the high voltage set up in this machine? Explain.

(a) Define electric flux. Write the S.I. units. (b) Using Gauss's law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it. (c) How is the field directed if (i) the sheet is positively charged, (ii) negat …