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Physics · Class 12 Science

Ch 4Moving Charges and Magnetism — Class 12 Physics, concept-first.

For over 2000 years, electricity and magnetism were studied as separate phenomena. This changed in 1820, when Danish physicist Hans Christian Oersted showed they were intimately connected.

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Key concepts

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Magnetic Force Balance

When a current-carrying wire or coil sits in a magnetic field, it feels a force (or, for a point charge, ). On its own that force just pushes the conductor - but in many real situations the push is deliberately set up to…

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

4.1

Introduction

For over 2000 years, electricity and magnetism were studied as separate phenomena. This changed in 1820, when Danish physicist Hans Christian Oersted showed they were intimately connected.

4.2

Magnetic Force

Magnetism is a force that acts on moving charges. A stationary charge experiences no magnetic force. The magnetic force on a charge depends on three things: the charge itself, its velocity, and the ma…

4.2.1

Sources and Fields

The interaction between two electric charges is understood in two stages: 1. The source charge creates an electric field in the space around it. 2.

4.2.2

Magnetic Field, Lorentz Force

When a charged particle moves through a region containing both an electric field and a magnetic field , the total force acting on it is the sum of the electric force and the magnetic force.

4.2.3

Magnetic Force on a Current-carrying Conductor

A current in a wire is simply a stream of moving charges. Since a magnetic field exerts a force on each moving charge, it also exerts a net force on the entire current-carrying wire.

+Worked Examplesi2 questions
  1. Example 4.1A straight wire of mass $200\ \text{g}$ and length $1.5\ \text{m}$ carries a current of $2\ \text{A}$. It is suspended in mid-air by a unifo…Free
  2. Example 4.2If the magnetic field is parallel to the positive $y$-axis and the charged particle is moving along the positive $x$-axis (Fig. 4.4), which…Preview
4.3

Motion in a Magnetic Field

The magnetic force is always perpendicular to the velocity of the charged particle. - Since work and , the magnetic force does zero work.

+Worked Examplesi1 question
  1. Example 4.3What is the radius of the path of an electron (mass $9 \times 10^{-31}\ \text{kg}$ and charge $1.6 \times 10^{-19}\ \text{C}$) moving at a s…Preview
4.4

Magnetic Field due to a Current Element, Biot-Savart Law

All magnetic fields arise from moving charges (currents) or intrinsic magnetic moments. The Biot-Savart law gives the magnetic field produced by a small, directed piece of current — a current element.

+Worked Examplesi1 question
  1. Example 4.4An element $\Delta \vec{l} = \Delta x\,\hat{i}$ is placed at the origin and carries a large current $I = 10\ \text{A}$ (Fig. 4.8). What is t…Preview
4.5

Magnetic Field on the Axis of a Circular Current Loop

A circular current loop produces a magnetic field that is symmetric about its axis. For any small current element on the loop, the Biot-Savart law gives a field contribution that is perpendicular to b…

+Worked Examplesi2 questions
  1. Example 4.5A straight wire carrying a current of $12\ \text{A}$ is bent into a semi-circular arc of radius $2.0\ \text{cm}$ as shown in Fig. 4.11(a). C…Free
  2. Example 4.6Consider a tightly wound $100$ turn coil of radius $10\ \text{cm}$, carrying a current of $1\ \text{A}$. What is the magnitude of the magnet…Preview
4.6

Ampere's Circuital Law

Ampere’s circuital law is an alternative, often simpler, way to express the same physics as the Biot-Savart law.

+Worked Examplesi1 question
  1. Example 4.7Figure 4.13 shows a long straight wire of a circular cross-section (radius $a$) carrying steady current $I$. The current $I$ is uniformly di…Preview
4.7

The Solenoid

A solenoid is a long wire wound into a tight helix. For it to be considered "long," its length must be much greater than its radius.

+Worked Examplesi1 question
  1. Example 4.8A solenoid of length $0.5\ \text{m}$ has a radius of $1\ \text{cm}$ and is made up of $500$ turns. It carries a current of $5\ \text{A}$. Wh…Preview
4.8

Force between Two Parallel Currents, the Ampere

A current-carrying conductor produces a magnetic field around it (Biot-Savart law). If another current-carrying conductor is placed in that field, the Lorentz force acts on the moving charges in the s…

+Worked Examplesi1 question
  1. Example 4.9The horizontal component of the earth's magnetic field at a certain place is $3.0 \times 10^{-5}\ \text{T}$ and the direction of the field i…Preview
4.9

Torque on Current Loop, Magnetic Dipole

A rectangular loop carrying current, placed in a uniform magnetic field, experiences a net torque that tends to rotate it.

4.9.1

Torque on a Rectangular Current Loop in a Uniform Magnetic Field

A rectangular loop carrying a steady current in a uniform magnetic field feels no net force but does experience a torque. This is analogous to an electric dipole in a uniform electric field.

+Worked Examplesi2 questions
  1. Example 4.10A $100$ turn closely wound circular coil of radius $10\ \text{cm}$ carries a current of $3.2\ \text{A}$. (a) What is the field at the centre…Free
  2. Example 4.11(a) A current-carrying circular loop lies on a smooth horizontal plane. Can a uniform magnetic field be set up in such a manner that the loo…Preview
4.9.2

Circular Current Loop as a Magnetic Dipole

A circular current loop behaves like a magnetic dipole when viewed from far away. This means its magnetic field pattern at large distances is identical to the electric field pattern of an electric dip…

4.10

The Moving Coil Galvanometer

A moving coil galvanometer (MCG) is a device used to detect and measure small electric currents. It works on the principle that a current-carrying coil placed in a magnetic field experiences a torque.…

+Worked Examplesi1 question
  1. Example 4.12In the circuit (Fig. 4.23) the current is to be measured. What is the value of the current if the ammeter shown (a) is a galvanometer with a…Preview

Summary

- Lorentz Force: Force on a charge moving with velocity in electric and magnetic fields: . For a current-carrying conductor, .

Points to Ponder

1. Closed loops vs. open lines: Electric field lines start on positive charges and end on negative charges (or go to infinity).

Exercises

+Show 13 questions13 questions
  1. 4.1A circular coil of wire consisting of $100$ turns, each of radius $8.0\ \text{cm}$ carries a current of $0.40\ \text{A}$. What is the magnit…Free
  2. 4.2A long straight wire carries a current of $35\ \text{A}$. What is the magnitude of the field $B$ at a point $20\ \text{cm}$ from the wire?Free
  3. 4.3A long straight wire in the horizontal plane carries a current of $50\ \text{A}$ in north to south direction. Give the magnitude and directi…Free
  4. 4.4A horizontal overhead power line carries a current of $90\ \text{A}$ in east to west direction. What is the magnitude and direction of the m…Preview
  5. 4.5What is the magnitude of magnetic force per unit length on a wire carrying a current of $8\ \text{A}$ and making an angle of $30^\circ$ with…Preview
  6. 4.6A $3.0\ \text{cm}$ wire carrying a current of $10\ \text{A}$ is placed inside a solenoid perpendicular to its axis. The magnetic field insid…Preview
  7. 4.7Two long and parallel straight wires A and B carrying currents of $8.0\ \text{A}$ and $5.0\ \text{A}$ in the same direction are separated by…Preview
  8. 4.8A closely wound solenoid $80\ \text{cm}$ long has $5$ layers of windings of $400$ turns each. The diameter of the solenoid is $1.8\ \text{cm…Preview
  9. 4.9A square coil of side $10\ \text{cm}$ consists of $20$ turns and carries a current of $12\ \text{A}$. The coil is suspended vertically and t…Preview
  10. 4.10Two moving coil meters, $M_1$ and $M_2$ have the following particulars: $R_1 = 10\ \Omega$, $N_1 = 30$, $A_1 = 3.6 \times 10^{-3}\ \text{m}^…Preview
  11. 4.11In a chamber, a uniform magnetic field of $6.5\ \text{G}$ ($1\ \text{G} = 10^{-4}\ \text{T}$) is maintained. An electron is shot into the fi…Preview
  12. 4.12In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electr…Preview
  13. 4.13(a) A circular coil of $30$ turns and radius $8.0\ \text{cm}$ carrying a current of $6.0\ \text{A}$ is suspended vertically in a uniform hor…Preview

Exemplar Problems

Higher-order thinking / exemplar-style practice problems.

+Show 27 questions27 questions
  1. Q1Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field $\vec{B} = B_0\hat{k}$. (a…Free
  2. Q2Biot-Savart law indicates that the moving electrons (velocity $\vec{v}$) produce a magnetic field $\vec{B}$ such that (a) $\vec{B} \perp \ve…Free
  3. Q3A current carrying circular loop of radius $R$ is placed in the $x$-$y$ plane with centre at the origin. Half of the loop with $x > 0$ is no…Free
  4. Q4An electron is projected with uniform velocity along the axis of a current carrying long solenoid. Which of the following is true? (a) The e…Preview
  5. Q5A circular current loop of magnetic moment $M$ is in an arbitrary orientation in an external magnetic field $\vec{B}$. The work done to rota…Preview
  6. Q6The gyro-magnetic ratio of an electron in an H-atom, according to Bohr model, is (a) independent of which orbit it is in. (b) negative. (c)…Preview
  7. Q7Consider a wire carrying a steady current, $I$ placed in a uniform magnetic field $\vec{B}$ perpendicular to its length. Consider the charge…Preview
  8. Q8Two identical current carrying coaxial loops, carry current $I$ in an opposite sense. A simple amperian loop passes through both of them onc…Preview
  9. Q9A cubical region of space is filled with some uniform electric and magnetic fields. An electron enters the cube across one of its faces with…Preview
  10. Q10A charged particle would continue to move with a constant velocity in a region wherein, (a) $E = 0,\ B \neq 0$. (b) $E \neq 0,\ B \neq 0$. (…Preview
  11. Q11Verify that the cyclotron frequency $\omega = eB/m$ has the correct dimensions of $[T]^{-1}$.Preview
  12. Q12Show that a force that does no work must be a velocity dependent force.Preview
  13. Q13The magnetic force depends on $\vec{v}$ which depends on the inertial frame of reference. Does then the magnetic force differ from inertial…Preview
  14. Q14Two long straight wires carry steady currents $I_1$ and $I_2$. The wire carrying $I_1$ lies along the $x$-axis with its current flowing in t…Preview
  15. Q15A current carrying loop consists of 3 identical quarter circles of radius $R$, lying in the positive quadrants of the $x$-$y$, $y$-$z$ and $…Preview
  16. Q16A charged particle of charge $e$ and mass $m$ is moving in an electric field $\vec{E}$ and magnetic field $\vec{B}$. Construct dimensionless…Preview
  17. Q17An electron enters with a velocity $\vec{v} = v_0\hat{i}$ into a cubical region (faces parallel to coordinate planes) in which there are uni…Preview
  18. Q18Do magnetic forces obey Newton's third law. Verify for two current elements $d\vec{l}_1 = dl\,\hat{i}$ located at the origin and $d\vec{l}_2…Preview
  19. Q19A galvanometer of resistance $10\ \Omega$ that gives maximum (full-scale) deflection for a current of $1\ \text{mA}$ is to be converted into…Preview
  20. Q20A long straight horizontal wire carrying a current of $25\ \text{A}$ rests fixed on a table. A second straight wire PQ of length $1\ \text{m…Preview
  21. Q21A rectangular coil ABCD of $100$ turns hangs vertically from one arm of a beam balance, with its lower horizontal side CD (length $1\ \text{…Preview
  22. Q22A rectangular conducting loop consists of two wires on two opposite sides of length $l$ joined together by rods of length $d$. The wires are…Preview
  23. Q23An electron and a positron are released from $(0, 0, 0)$ and $(0, 0, 1.5R)$ respectively, in a uniform magnetic field $\vec{B} = B_0\hat{i}$…Preview
  24. Q24A uniform conducting wire of length $12a$ and resistance $R$ is wound up as a current carrying coil in the shape of (i) an equilateral trian…Preview
  25. Q25Consider a circular current-carrying loop of radius $R$ in the $x$-$y$ plane with centre at origin. Consider the line integral $\Im(L) = \le…Preview
  26. Q26A galvanometer of resistance $10\ \Omega$ that gives maximum (full-scale) deflection for a current of $1\ \text{mA}$ is to be converted into…Preview
  27. Q27Five long straight parallel wires A, B, C, D and E, each carrying the same current $I$ out of the plane of the page, are placed along the fi…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 3 questions3 questions
  1. Q1Two protons of equal kinetic energies enter a region of uniform magnetic field. The first proton enters normal to the field direction while…Preview
  2. Q2(a) Define SI unit of current in terms of the force between two parallel current carrying conductors. (b) Two long straight parallel conduct…Preview
  3. Q3(a) State Biot - Savart law and express it in the vector form. (b) Using Biot - Savart law, obtain the expression for the magnetic field due…Preview