Magnetic Effects of Current — CBSE Class 12 board PYQs

Assertion (A): The energy of a charged particle moving in a magnetic field does not change.
Reason (R): It is because the work done by the magnetic force on the charge moving in a magnetic field is zero.

Beams of electrons and protons move parallel to each other in the same direction. They

A long straight wire of radius $a$ carries a steady current $I$ distributed uniformly across its cross-section. The ratio of the magnitudes of the magnetic field ${\vec{B}}_1$ at $\frac{a}{2}$ and ${\vec{B}}_2$ at a distance $2a$ from the axis is

The magnetic dipole moment of a current carrying coil does not depend upon:

Write the mathematical form of the Ampere-Maxwell circuital law.

A proton and an electron travelling along parallel paths enter a region of uniform magnetic field acting perpendicular to their paths. Which of them will move in a circular path with higher frequency?

Write the underlying principle of a moving coil galvanometer.

What can be the cause of helical motion of a charged particle?

Using the concept of force between two infinitely long parallel current-carrying conductors, define one ampere of current.

A beam of $\alpha$-particles projected along the $+x$-axis experiences a force due to a magnetic field along the $+y$-axis. What is the direction of the magnetic field?

A beam of electrons projected along the $+x$-axis experiences a force due to a magnetic field along the $+y$-axis. What is the direction of the magnetic field?

A beam of protons projected along the $+x$-axis experiences a force due to a magnetic field along the $-y$-axis. What is the direction of the magnetic field?

An electron does not suffer any deflection while passing through a region of uniform magnetic field. What is the direction of the magnetic field?

Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why?

What is the direction of the force acting on a charged particle $q$ moving with velocity $\vec{v}$ in a uniform magnetic field $\vec{B}$?

An electron beam projected along the $+X$-axis experiences a force due to a magnetic field along the $+Y$-axis. What is the direction of the magnetic field?

Two wires of equal length are bent in the form of two loops. One loop is square shaped, the other is circular. They are suspended in a uniform magnetic field and the same current is passed through them. Which loop will experience the greater torque? Give reasons.

Under what condition does an electron moving through a magnetic field experience maximum force?

Under what condition is the force acting on a charge moving through a uniform magnetic field minimum?

(i) State and explain Ampere's circuital law.
(ii) Two long straight parallel wires separated by $20\text{cm}$ carry $5\text{A}$ and $10\text{A}$ current respectively in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between …

Derive an expression for the magnetic force $\vec{F}$ acting on a straight conductor of length $L$ carrying current $I$ in an external magnetic field $\vec{B}$. Is it valid when the conductor is in zig-zag form? Justify.

Briefly explain why and how a galvanometer is converted into an ammeter.

Two long straight parallel wires A and B separated by a distance $d$ carry equal currents $I$ flowing in the same direction.
(a) Find the magnetic field at a point P situated between them at a distance $x$ from one wire.
(b) Show graphically the variation of the magnetic field wi …

(a) Write an expression for the magnetic moment associated with a current ($I$) carrying circular coil of radius $r$ having $N$ turns.
(b) Consider the above coil placed in the YZ-plane with its centre at the origin. Derive an expression for the magnetic field due to it at the po …

(a) Define current sensitivity of a galvanometer. Write its expression. (b) A galvanometer has resistance $G$ and shows full-scale deflection for current $I_g$. (i) How can it be converted into an ammeter to measure current up to $I_0(I_0>I_g)$? (ii) What is the effective resis …

State the underlying principle of a cyclotron. Explain its working with the help of a schematic diagram. Obtain the expression for the cyclotron frequency.

A charged particle $q$ is moving in the presence of a magnetic field $B$ which is inclined at an angle $30^{\circ }$ with the direction of motion of the particle. Draw the trajectory followed by the particle in the presence of the field and explain how the particle describes this …

A charge $q$ of mass $m$ is moving with velocity $v$ at right angles to a uniform magnetic field $B$. Deduce the expression for the radius of the circular path it describes.

State Lorentz's force and express it in vector form. Which pair of vectors are always perpendicular to each other? Derive the expression for the force acting on a current-carrying conductor of length $L$ in a uniform magnetic field $B$.

An electron of mass $m_e$ revolves around a nucleus of charge $+Ze$. Show that it behaves like a tiny magnetic dipole. Hence prove that the magnetic moment associated with it is $\vec{\mu }=-\frac{e}{2m_e}\vec{L}$, where $\vec{L}$ is the orbital angular momentum of the electron …

State Ampere's circuital law. Use this law to find the magnetic field due to a straight infinite current-carrying wire. How are the magnetic field lines different from electrostatic field lines?

State the principle of a cyclotron. Show that the time period of revolution of particles in a cyclotron is independent of their speeds. Why is this property necessary for the operation of a cyclotron?

(a) Write the expression for the magnetic force acting on a charged particle moving with velocity $v$ in the presence of a magnetic field $B$.
(b) A neutron, an electron and an alpha particle moving with equal velocities enter a uniform magnetic field going into the plane of the …

Two long straight parallel conductors carry steady currents $I_1$ and $I_2$ separated by a distance $d$. If the currents flow in the same direction, show how the magnetic field set up in one produces an attractive force on the other. Obtain the expression for this force. Hence de …

State the principle of working of a galvanometer. A galvanometer of resistance $G$ is converted into a voltmeter to measure up to $V$ volts by connecting a resistance $R_1$ in series with the coil. If resistance $R_2$ is connected in series instead, it can measure up to $V/2$ vol …

Two identical circular wires P and Q, each of radius $R$ and carrying current $I$, are kept in perpendicular planes such that they have a common centre. Find the magnitude and direction of the net magnetic field at the common centre of the two coils.

A rectangular loop of wire of size $4\text{cm}\times 10\text{cm}$ carries a steady current of $2\text{A}$. A straight long wire carrying $5\text{A}$ current is kept near the loop, coplanar with it, as shown. Find
(i) the torque acting on the loop and
(ii) the magnitude and …

Write the expression for the Lorentz magnetic force on a particle of charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$. Show that no work is done by this force on the charged particle.

A steady current $I_1$ flows through a long straight wire. Another wire carrying a steady current $I_2$ in the same direction is kept close and parallel to the first wire. Show with the help of a diagram how the magnetic field due to the current $I_1$ exerts a magnetic force on t …

A wire AB carries a steady current of $6\text{A}$ and is lying on a table. Another wire CD carrying $4\text{A}$ is held directly above AB at a height of $1\text{mm}$. Find the mass per unit length of wire CD so that it remains suspended at its position when left free. Give …

A square coil of side $10\text{cm}$ has 20 turns and carries a current of $12\text{A}$. The coil is suspended vertically and the normal to its plane makes an angle of $30^{\circ }$ with the direction of a uniform horizontal magnetic field. If the torque experienced by the coil e …

Write the expression for the magnetic moment $\vec{m}$ due to a planar square loop of side $\ell$ carrying a steady current $I$ in vector form. This loop is placed in a horizontal plane near a long straight conductor carrying a steady current $I_1$ at a distance $\ell$ as shown. …

A long straight wire of circular cross-section of radius $a$ carries a steady current $I$ distributed uniformly across the cross-section. Apply Ampere's circuital law to calculate the magnetic field at a point $r$ for
(i) $r<a$ and
(ii) $r>a$.

State the underlying principle of working of a moving coil galvanometer. Write two reasons why a galvanometer cannot be used as such to measure current in a given circuit. Name any two factors on which the current sensitivity of a galvanometer depends.

Define current sensitivity and voltage sensitivity of a galvanometer. Justify the statement that increasing the current sensitivity may not necessarily increase the voltage sensitivity of a galvanometer.

A charge $q$ moving along the X-axis with velocity $\vec{v}$ is subjected to a uniform magnetic field $B$ acting along the Z-axis as it crosses the origin O. (i) Trace its trajectory. (ii) Does the charge gain kinetic energy as it enters the magnetic field? Justify your answer.

State Biot-Savart's law. A current $I$ flows in a conductor placed perpendicular to the plane of the paper. Indicate the direction of the magnetic field due to a small element $d\vec{\ell }$ at a point P situated at a distance $\vec{r}$ from the element.

Using Ampere's circuital law, derive an expression for the magnetic field along the axis of a toroidal solenoid.

Write the relation for the force acting on a charge carrier $q$ moving with velocity $\vec{v}$ through a magnetic field $\vec{B}$ in vector notation. Using this relation, deduce the condition under which this force will be
(i) maximum and
(ii) minimum.

Which of the two, an ammeter or a milliammeter, has a higher resistance and why?

State the principle of working of a cyclotron. Write two uses of this machine.

How do you convert a galvanometer into an ammeter? Why is an ammeter always connected in series?

A galvanometer with a coil of resistance $120\Omega$ shows full-scale deflection for a current of $2.5\text{mA}$. How will you convert the galvanometer into an ammeter of range $0$ to $7.5\text{A}$? Determine the net resistance of the ammeter. When an ammeter is put in a ci …

Two long parallel straight wires X and Y separated by a distance of $5\text{cm}$ in air carry currents of $10\text{A}$ and $5\text{A}$ respectively in opposite directions. Calculate the magnitude and direction of the force on a $20\text{cm}$ length of the wire Y.

An electron moving with a velocity $\vec{v}=(1.0\times 10^7\text{m/s})\hat{i}+(0.5\times 10^7\text{m/s})\hat{j}$ enters a region of uniform magnetic field $\vec{B}=(0.5\text{mT})\hat{j}$. Find the radius of the circular path described by it. While rotating, does …

Briefly explain the various ways to increase the strength of the magnetic field produced by a given solenoid.

(a) Derive the expression for the torque acting on the rectangular current-carrying coil of a galvanometer. Why is the magnetic field made radial?
(b) An $\alpha$-particle is accelerated through a potential difference of $10\text{kV}$ and moves along the x-axis. It enters a reg …

Two infinitely long straight wires $A_1$ and $A_2$ carrying currents $I$ and $2I$ flowing in the same direction are kept a distance '$d$' apart. Where should a third straight wire $A_3$ carrying current $1.5I$ be placed between $A_1$ and $A_2$ so that it experiences no net forc …

(a) State Ampere's circuital law. Use this law to obtain the expression for the magnetic field inside an air-cored toroid of average radius $r$, having $n$ turns per unit length and carrying a steady current $I$.
(b) An observer to the left of a solenoid of $N$ turns, each of cro …

(a) Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of the velocity or energy of the particle.
(b) Draw a schematic sketch of a cyclotron. Explain, giving the essential details of its construction, how …

(a) Draw a labelled diagram of a moving coil galvanometer. Describe briefly its principle and working. (b) Answer the following: (i) Why is it necessary to introduce a cylindrical soft iron core inside the coil of a galvanometer? (ii) Increasing the current sensitivity of a galva …

(a) Using Biot-Savart's law, derive the expression for the magnetic field in vector form at a point on the axis of a circular current loop.
(b) What does a toroid consist of? Find the expression for the magnetic field inside a toroid of $N$ turns, average radius $r$, carrying a c …

(a) Draw a schematic sketch of a cyclotron. Explain clearly the role of the crossed electric and magnetic fields in accelerating the charge. Hence derive the expression for the kinetic energy acquired by the particles. (b) An $\alpha$-particle and a proton are released from the c …

(a) Write the expression for the force $\vec{F}$ acting on a charged particle of charge $q$ moving with velocity $\vec{v}$ in the presence of both an electric field $\vec{E}$ and a magnetic field $\vec{B}$. Obtain the condition under which the particle moves undeflected through t …

(a) Explain, giving reasons, the basic difference in converting a galvanometer into (i) a voltmeter and (ii) an ammeter. (b) Two long straight parallel conductors carrying steady currents $I_1$ and $I_2$ are separated by a distance $d$. Explain briefly, with a suitable diagram, h …

(a) State the principle and the working of a moving coil galvanometer, giving its labelled diagram.
(b) Justify the statement: increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity.
(c) Outline the necessary steps to convert a g …

(a) Using Ampere's circuital law, obtain the expression for the magnetic field due to a long solenoid at a point inside the solenoid on its axis.
(b) In what respect is a toroid different from a solenoid? Draw and compare the pattern of magnetic field lines in the two cases.
(c) …

Draw a schematic sketch of a cyclotron. Explain briefly how it works and how it is used to accelerate charged particles.
(i) Show that the time period of ions in a cyclotron is independent of both the speed and the radius of the circular path.
(ii) What is the resonance condition …

(a) Two straight long parallel conductors carry currents $I_1$ and $I_2$ in the same direction. Deduce the expression for the force per unit length between them and depict the pattern of magnetic field lines around them. (b) A rectangular current-carrying loop EFGH is kept in a u …

State Biot-Savart law. Use it to derive an expression for the magnetic field at the centre of a circular loop of radius $R$ carrying a steady current $I$. Sketch the magnetic field lines for such a current-carrying loop.

With the help of a neat and labelled diagram, explain the underlying principle and working of a moving coil galvanometer. What is the function of
(i) the uniform radial field and
(ii) the soft iron core in such a device?

Derive a mathematical expression for the force per unit length experienced by each of two long current-carrying conductors placed parallel to each other in air. Hence define one ampere of current. Explain why two parallel straight conductors carrying current in opposite direction …

(a) With the help of a labelled diagram, explain the principle and working of a moving coil galvanometer.
(b) Two parallel coaxial circular coils of equal radius $R$ and equal number of turns $N$ carry equal currents $I$ in the same direction and are separated by a distance $2R$. …

(a) State Biot-Savart's law. Using this law, derive the expression for the magnetic field due to a current-carrying circular loop of radius $R$ at a point at a distance $x$ from its centre along the axis of the loop. (b) Two small identical circular loops (1) and (2), carrying eq …

Explain the principle and working of a cyclotron with the help of a labelled diagram. A cyclotron's oscillator frequency is $10\text{MHz}$. What should be the operating magnetic field for accelerating protons? If the radius of its dees is $60\text{cm}$, what is the kinetic en …

Depict the magnetic field lines due to two straight, long, parallel conductors carrying currents $I_1$ and $I_2$ in the same direction. Hence deduce an expression for the force acting per unit length on one conductor due to the other. Is this force attractive or repulsive? A rect …