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Physics · Class 12 Science

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

The previous two sub-topics of this unit built up electrostatics -- the field and potential produced by charges AT REST. This sub-topic turns to what happens once charge is allowed to MOVE: a moving charge, or an electric current (which is simply charge in organised, continuous motion through a conductor), is found to…

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Key concepts

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Oersted's Experiment and the Right-Hand Rules

In 1820, Hans Christian Oersted discovered that a current-carrying wire deflects a nearby compass needle, and that reversing the current reverses the deflection -- proof that a steady current is itself a source of magnet…

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In previous exams

How often this chapter’s concepts have been examined — real appearance data, never estimated.

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3 concepts · 3 appearances

2026, 2024, 2021

Chapter contents

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

4.1

Introduction

The previous two sub-topics of this unit built up electrostatics -- the field and potential produced by charges AT REST.

4.2

Concept of Magnetic Field and Oersted's Experiment

A magnetic field, denoted , is the region of space surrounding a magnet or a current-carrying conductor in which a magnetic pole, a small compass needle, a moving charge, or another current-carrying c…

4.3

Biot-Savart Law

Oersted's experiment (Section 4.2) established, qualitatively, that a current-carrying conductor produces a magnetic field circling around it.

4.4

Magnetic Field Due to a Straight Current-Carrying Conductor

Setting up the integral. Consider a long straight wire carrying current , and a field point at perpendicular distance from the wire.

4.5

Magnetic Field at the Centre and on the Axis of a Circular Current Loop

Field at the centre of a circular loop. Consider a circular loop of wire of radius carrying current , and the field point taken at the loop's own centre.

4.6

Ampere's Circuital Law

Statement of the law. Ampere's circuital law states that, for any closed loop (called an Amperian loop) drawn in space, the line integral of the magnetic field around that loop equals times the total…

4.7

Magnetic Field of a Straight Solenoid

The solenoid. A solenoid is a long, cylindrical coil formed by winding an insulated wire into many closely spaced, essentially circular turns, one after another along the length of a cylinder.

4.8

Lorentz Force: Force on a Moving Charge in Electric and Magnetic Fields

Force due to a magnetic field alone. A charge moving with velocity through a region containing a magnetic field experiences a magnetic force

4.9

Motion of a Charged Particle in a Perpendicular Magnetic Field: The Cyclotron

Circular motion in a perpendicular field. From Section 4.8, a charged particle moving with speed exactly perpendicular to a uniform magnetic field feels a magnetic force of constant magnitude , always…

4.10

Force on a Current-Carrying Conductor in a Magnetic Field

From individual charge carriers to the whole conductor. A current-carrying conductor contains a very large number of free charge carriers (electrons, in a metal), each drifting with some small average…

4.11

Force Between Two Parallel Current-Carrying Conductors and the Definition of Ampere

Setting up the mutual-force calculation. Consider two long, straight, parallel conductors, separated by a perpendicular distance , carrying currents and respectively.

4.12

Torque on a Current Loop in a Uniform Magnetic Field

Setup: a rectangular loop in a uniform field. Consider a single rectangular current loop , of sides and (area ), carrying current , free to rotate about an axis through its centre, placed in a uniform…

4.13

Moving Coil Galvanometer and Current Sensitivity

Construction. A moving-coil galvanometer consists of a small rectangular (or circular) coil of many turns of fine insulated wire, wound on a light metallic (usually aluminium) frame, suspended or pivo…

4.14

Conversion of Galvanometer into Ammeter and Voltmeter

A bare galvanometer coil, exactly as constructed in Section 4.13, is a delicate instrument: its fine wire can safely carry only a very small current (typically in the milliampere range, called its ful…

Summary

This sub-topic developed WBCHSE Unit 3's first half, moving charges and magnetism, from Oersted's original discovery through to a working ammeter and voltmeter.

Sample & Board Papers

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

+Show 28 questions28 questions
  1. Q1What should be the value of the shunt to be connected in parallel to a galvanometer of resistance G, so that 1/n part of the main current wi…Preview
  2. Q2In a compact coil of 50 turns, the current strength is 10A and the radius of the coil is 25×10⁻² meter. Find the magnitude of the magnetic f…Preview
  3. Q3In a hydrogen atom, an electron of charge e revolves in an orbit of radius r with speed v. Find the magnitude of the resulting magnetic mome…Preview
  4. Q4With an accompanying diagram, write down Biot-Savart's law in vector form. Can a cyclotron accelerate neutrons? **OR** Define magnetic perme…Preview
  5. Q5A conducting circular loop of radius r carries a constant current I. It is placed in a uniform magnetic field B such that B is perpendicular…Preview
  6. Q6Dimension of magnetic flux is (a) [ML²T⁻²A⁻¹] (b) [MLT⁻¹A⁻²] (c) [ML⁻¹TA⁻¹] (d) [MT⁻¹A]Preview
  7. Q7What do you mean by magnetic flux density? **OR** What is Q-factor?Preview
  8. Q8What is the magnitude of force experienced by a stationary charge placed in a uniform magnetic field? **OR** If an electron is not deflected…Preview
  9. Q9A copper wire of length l metre is bent to form a circular loop. If i amp current flows through the loop, find out the magnitude of magnetic…Preview
  10. Q10a) Derive an expression for the torque on a rectangular coil of area A carrying a current I and placed in a uniform magnetic field B. Indica…Preview
  11. Q11(a) State Ampere's circuital law. (b) Use Ampere's circuital law to obtain the magnetic field inside a toroid. (c) A solenoid of length 1.0…Preview
  12. Q12A charged particle is moving in a uniform magnetic field in a circular path of radius R. When energy of the particle is doubled, then the ne…Preview
  13. Q13Under the influence of a uniform magnetic field, a charged particle is moving in a circle of radius R with constant speed V. The time period…Preview
  14. Q14How is a galvanometer converted into an ammeter? **OR** Can neutrons be accelerated in a cyclotron? Why?Preview
  15. Q15Write down the vector form of Biot-Savart's law. Using this law, derive an expression for the magnetic field at the centre of a circular coi…Preview
  16. Q16A current carrying long erect wire is kept at an angle θ with an external uniform magnetic field. The wire experiences highest force if (a)…Preview
  17. Q17A particle of charge q moves with a velocity v at angle θ to a magnetic field B. What is the force experienced by the particle? **OR** What…Preview
  18. Q18A circular coil of 200 turns and radius 0.2 m carries a current of 14 A. What is the magnitude of magnetic moment associated with the coil?Preview
  19. Q19State Ampere's circuital law. By applying this law, obtain an expression for the magnetic field at a point well inside the solenoid carrying…Preview
  20. Q20A charged particle is moving in a uniform magnetic field in a circular path of radius R. If the energy of the particle is doubled, then the…Preview
  21. Q21Two circular loops having ratio of their radii 1 : 2 possess same magnetic moment. The ratio of their circulating currents will be (a) 4 : 1…Preview
  22. Q22What is the magnitude of force experienced by a charge at rest placed in a uniform magnetic field? **OR** Between ammeter and voltmeter, whi…Preview
  23. Q23(a) An electron moves with velocity 10⁷ ms⁻¹ in the direction perpendicular to the magnetic field of 10⁻³ T. Determine the magnetic force ac…Preview
  24. Q24If the radius of an ideal solenoid be r and magnetic field intensity on its axis according to Ampere's circuital law be B, then (a) B ∝ r (b…Preview
  25. Q25The resistance of a voltmeter is 300 Ω. It can measure the highest potential difference of 150 volt. The resistance that should be connected…Preview
  26. Q26For a semicircular conductor ( shown in the diagram ) the magnetic field at the centre of the conductor is (a) μ₀i/2a (b) μ₀i/2πa (c) zero (…Preview
  27. Q27The ratio of the radii of two circular loops is 1 : 2. The ratio of their magnetic moments is 1 : 2. The ratio of currents flowing through t…Preview
  28. Q28The force acting between two parallel current carrying wires is F. If the current through each wire is doubled and separation becomes three…Preview

More questions

30 Q
+Show 10 questions10 questions
  1. Example 1Describe Oersted's experiment in brief and state what it demonstrated about the relationship between electricity and magnetism.Free
  2. Example 2State the Biot-Savart law in symbolic form for the magnetic field $d\vec{B}$ due to a current element $I\,d\vec{l}$, and write the SI value…Free
  3. Example 3A single circular turn of wire of radius $10\ \text{cm}$ carries a current of $5\ \text{A}$. Find the magnetic field at the centre of the lo…Free
  4. Example 4Using Ampere's circuital law, find the magnetic field at a perpendicular distance of $5\ \text{cm}$ from a long straight wire carrying a cur…Preview
  5. Example 5A long solenoid has $1000$ turns per metre and carries a current of $2\ \text{A}$. Find the magnetic field inside it, well away from its end…Preview
  6. Example 6A charge of $2\ \mu\text{C}$ moves with a speed of $3\times 10^{4}\ \text{m/s}$ perpendicular to a magnetic field of $0.5\ \text{T}$. Find t…Preview
  7. Example 7A proton ($q = 1.6\times 10^{-19}\ \text{C}$, $m = 1.67\times 10^{-27}\ \text{kg}$) moves in a cyclotron operating at a magnetic field of $1…Preview
  8. Example 8A straight conductor of length $0.5\ \text{m}$ carries a current of $4\ \text{A}$ and is placed perpendicular to a uniform magnetic field of…Preview
  9. Example 9Two long, straight, parallel wires $0.1\ \text{m}$ apart each carry a current of $5\ \text{A}$ in the same direction. Find the force per uni…Preview
  10. Example 10A rectangular coil of $50$ turns and area $0.02\ \text{m}^2$ carries a current of $2\ \text{A}$ and is placed in a uniform magnetic field of…Preview
+Show 10 questions10 questions
  1. Q11Explain the concept of a magnetic field as a vector field, and state what kind of source produces it, contrasting this with the source of an…Free
  2. Q12Describe Oersted's experiment in detail -- the apparatus used, the observation made, and how the deflection depended on the direction of the…Free
  3. Q13State the Biot-Savart law in full vector form and explain, using the right-hand rule, how the direction of $d\vec{B}$ is determined from the…Free
  4. Q14Using the Biot-Savart law, derive the expression for the magnetic field at the centre of a circular current loop of radius $R$ carrying curr…Preview
  5. Q15Derive the expression for the magnetic field at a point on the axis of a circular current loop, at a distance $x$ from its centre, and show…Preview
  6. Q16State Ampere's circuital law in integral form and compare it, as a calculation tool, with Gauss's law of electrostatics.Preview
  7. Q17Using Ampere's circuital law, derive the expression for the magnetic field at a perpendicular distance $r$ from a long, straight, current-ca…Preview
  8. Q18Using Ampere's circuital law, derive the expression for the magnetic field inside a long, straight solenoid, stating clearly the assumptions…Preview
  9. Q19Derive an expression for the radius of the circular path traced by a charged particle moving with speed $v$ perpendicular to a uniform magne…Preview
  10. Q20Explain the working principle of a moving-coil galvanometer, define its current sensitivity, and state two distinct ways of increasing it.Preview
+Show 10 questions10 questions
  1. Q21A long straight wire carries a current of $15\ \text{A}$. Find the magnetic field at a point $20\ \text{cm}$ from the wire.Free
  2. Q22A circular coil of $100$ turns and radius $5\ \text{cm}$ carries a current of $0.5\ \text{A}$. Find the magnetic field at the centre of the…Free
  3. Q23A circular loop of radius $3\ \text{cm}$ carries a current of $4\ \text{A}$. Find the magnetic field at a point on the axis of the loop, $4\…Free
  4. Q24A solenoid of length $0.5\ \text{m}$ has $800$ turns of wire and carries a current of $3\ \text{A}$. Find the magnetic field inside it, well…Preview
  5. Q25Two long parallel wires $15\ \text{cm}$ apart carry currents of $10\ \text{A}$ and $15\ \text{A}$ in opposite directions. Find the force per…Preview
  6. Q26A proton moving with a velocity of $2\times 10^{6}\ \text{m/s}$ enters, at right angles, a uniform magnetic field of $0.4\ \text{T}$. Find (…Preview
  7. Q27A deuteron ($q = 1.6\times 10^{-19}\ \text{C}$, $m = 3.34\times 10^{-27}\ \text{kg}$) is accelerated in a cyclotron whose magnetic field is…Preview
  8. Q28A straight conductor of length $0.8\ \text{m}$ carries a current of $6\ \text{A}$ and is placed in a uniform magnetic field of $0.3\ \text{T…Preview
  9. Q29A rectangular coil of sides $4\ \text{cm}$ and $6\ \text{cm}$, having $200$ turns, carries a current of $1\ \text{A}$ and is placed with its…Preview
  10. Q30A galvanometer of resistance $50\ \Omega$ gives full-scale deflection for a current of $5\ \text{mA}$. Find (a) the shunt resistance needed…Preview