Physics Class 12 Part I…
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Bar Magnet Magnetic Field

🎓 Class 12 Physics CBSE Theory Ch 5 – Magnetism and Matter ⏱ ~14 min
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Bar Magnet Magnetic Field

5.1 Introduction

The word magnet comes from a Greek island, Magnesia, where iron-rich stones called lodestones attracted bits of iron more than 2000 years ago. Centuries later, sailors discovered that a freely-suspended sliver of lodestone always pointed roughly north - the first magnetic compass.

In Chapter 4 you learnt that moving charges produce magnetic fields. In this chapter we explore the magnetism of matter itself - bar magnets, the Earth, and the diamagnetic, paramagnetic and ferromagnetic substances around us. We start with the simplest magnet of all: a bar magnet.

Some easily verified facts about magnets:
  • Every magnet has two poles, called the north (N) and south (S) poles.
  • Like poles repel; unlike poles attract.
  • Magnetic monopoles do not exist - if you cut a bar magnet in half, each piece is itself a complete magnet with both N and S poles.
  • Iron, cobalt, nickel and several alloys can be magnetised; most other substances cannot easily be made into magnets.

5.2 The Bar Magnet

5.2.1 Magnetic field lines

Sprinkle iron filings on a sheet of paper placed over a bar magnet and tap gently. The filings line up along curves leaving one pole and re-entering the other. These curves trace the magnetic field lines of the magnet.

N S Field lines emerge from N and re-enter at S; inside, they go S to N forming closed loops.
Fig 5.1 Magnetic field lines of a bar magnet (analogous to the iron-filings pattern).
Properties of magnetic field lines:
  1. They form continuous closed loops (unlike electric field lines which start on +q and end on -q).
  2. The tangent at any point gives the direction of \(\vec B\) there.
  3. Density of lines (lines per unit area) gives the magnitude of \(\vec B\).
  4. Field lines never cross - the field has a unique direction everywhere.

5.2.2 Bar magnet as an equivalent solenoid

You saw in Chapter 4 that a current-carrying solenoid produces a magnetic field very similar to that of a bar magnet. This deep similarity is no coincidence - inside the bar magnet, atomic-scale current loops (orbiting electrons + electron spin) collectively act like the loops of a solenoid. The N and S poles of the bar magnet correspond to the two ends of the solenoid.

N S Bar magnet N S Solenoid carrying current I
Fig 5.2 The magnetic field outside a solenoid is essentially that of a bar magnet.

5.2.3 Magnetic dipole moment

Both a bar magnet and a current-carrying loop are described by a single vector - the magnetic dipole moment \(\vec m\). For a uniform bar magnet of pole strength \(q_m\) and length \(2l\),

\[\vec m = q_m\,(2\vec l)\]

where \(2\vec l\) points from S to N. The SI unit of m is A m\(^2\) (or J/T). For a current loop, m = NIA.

5.2.4 Magnetic field on the axis of a bar magnet (axial field)

At a point on the axis of a magnet at distance r from its centre (with r >> l, the short-magnet limit):

\[B_{axial} = \dfrac{\mu_0}{4\pi}\,\dfrac{2m}{r^3}\]

The field points along the dipole moment (S → N direction).

5.2.5 Magnetic field on the equator of a bar magnet (equatorial field)

At a point on the perpendicular bisector at distance r >> l:

\[B_{equatorial} = \dfrac{\mu_0}{4\pi}\,\dfrac{m}{r^3}\]

The field points opposite to \(\vec m\) (N → S direction). Note that the axial field is exactly twice the equatorial field at the same distance - the same 2:1 ratio you saw for the electric dipole.

N S P (axial) B Q (equatorial) B r r
Fig 5.3 Axial point P and equatorial point Q of a bar magnet. Note B at P points along m; B at Q opposite to m.

5.2.6 Torque on a magnetic dipole in a uniform field

A bar magnet of moment \(\vec m\) placed in a uniform external field \(\vec B\) experiences a torque (no net force) trying to align m with B:

\[\vec\tau = \vec m \times \vec B,\qquad \tau = mB\sin\theta\]

The associated potential energy is

\[U = -\vec m\cdot\vec B = -mB\cos\theta\]

U is minimum (= -mB) when m is parallel to B, maximum (= +mB) when antiparallel. Stable equilibrium ⇒ θ = 0; unstable equilibrium ⇒ θ = 180°.

Worked Example 5.1 - Axial field

Example 5.1 L3 Apply

A short bar magnet has dipole moment m = 0.40 A m\(^2\). Find the magnetic field at a point on its axis 10 cm from its centre.

r = 0.10 m, μ\(_0\)/4π = 10\(^{-7}\) T m/A.

\(B_{axial} = (10^{-7})\dfrac{2(0.40)}{(0.10)^3} = (10^{-7})(800) = 8.0\times10^{-5}\) T.

The field points along m, i.e. from S → N of the magnet.

Worked Example 5.2 - Equatorial field & ratio

Example 5.2 L3 Apply

For the same magnet (m = 0.40 A m²) find B at 10 cm on the equator. What is \(B_{axial}/B_{equatorial}\)?

\(B_{eq} = (10^{-7})(0.40)/(0.10)^3 = 4.0\times10^{-5}\) T (along S → N opposite to m).

Ratio: \(B_{axial}/B_{eq} = 8.0/4.0 = 2\). The axial field is twice the equatorial field at the same distance, regardless of m.

Interactive: Bar-Magnet Field Calculator L3 Apply

Drag sliders to set dipole moment m and distance r; see axial and equatorial fields update.

\(B_{axial}\) = 80.0 μT  |  \(B_{eq}\) = 40.0 μT
N S P Q
Activity 5.1 - Mapping a bar-magnet field with iron filingsL4 Analyse

You will need: a bar magnet, white paper, iron filings (or finely powdered steel wool).

  1. Place the bar magnet on a flat surface and cover it with the white paper.
  2. Sprinkle iron filings uniformly on the paper.
  3. Tap the paper gently. Sketch the pattern you observe.
Predict: Where are the filings densest? Where do they thin out? Will the lines ever cross?

The filings concentrate near the poles (where field lines crowd) and thin out at the equator. They form smooth curves that emerge from N and re-enter S without ever crossing - because B has a unique direction at every point in space.

Competency-Based Questions L1-L6

A short bar magnet of moment 0.5 A m² is placed in air. A small compass is moved around it, and the field B is measured at various distances and orientations.
1. The compass needle aligns with B. At a point 20 cm on the magnet's axis, what is B? L3 Apply
  • (a) 1.25 × 10⁻⁵ T
  • (b) 6.25 × 10⁻⁶ T
  • (c) 2.5 × 10⁻⁵ T
  • (d) 5.0 × 10⁻⁵ T
(a) B = 10⁻⁷ × 2 × 0.5/(0.20)³ = 1.25 × 10⁻⁵ T.
2. State two ways in which magnetic field lines differ from electric field lines. L2 Understand
(i) Magnetic field lines form closed loops; electric field lines start and end on charges. (ii) Magnetic field lines exist inside the source (e.g. inside a magnet); electric field lines do not pass through the interior of a charge.
3. True/False: When a bar magnet is cut into two halves, you obtain isolated north and south magnetic monopoles. L1 Remember
False. Each piece is a complete magnet with its own pair of N-S poles; magnetic monopoles have never been observed.
4. Why is the axial field twice the equatorial field at the same distance? Discuss using the geometry of dipoles. L4 Analyse
Both fields fall as 1/r³, but at the axial point the contributions of the two equivalent poles add directly (along the axis). At the equatorial point only the perpendicular components survive after vector addition - and these reduce by an extra factor of cos θ from each pole, halving the result.
5. Design an experiment to determine the magnetic dipole moment of an unknown bar magnet using a deflection magnetometer. L6 Create
Place a deflection magnetometer in the "tan A" position. Place the unknown magnet on the east-west arm at distance d. The compass deflects by θ where B_axial(magnet) = B_horizontal(Earth) tan θ. Measuring θ gives B_axial = (μ₀/4π)(2m/d³); since B_H is known (or can be measured separately), m can be calculated as m = B_H tan θ × d³/(2 × 10⁻⁷). Repeat at multiple distances and average.

Assertion-Reason Pairs L4 Analyse

Options: (A) Both true, R correct explanation. (B) Both true, R not the explanation. (C) A true, R false. (D) A false, R true.

Assertion: Magnetic field lines never intersect.
Reason: The direction of the magnetic field at a point is uniquely defined.
(A). If two field lines crossed, B would have two directions at that point - impossible.
Assertion: A bar magnet placed in a uniform field experiences only torque, not force.
Reason: The forces on the two poles are equal and opposite in a uniform field.
(A). Equal and opposite forces give zero net force but a non-zero couple.
Assertion: The potential energy of a magnetic dipole is minimum when m is antiparallel to B.
Reason: U = -mB cos θ.
(D). R is correct, but U is minimum at θ = 0° (parallel), not antiparallel. So A is false.

Frequently Asked Questions - Bar Magnet Magnetic Field

What is the main concept covered in Bar Magnet Magnetic Field?
In NCERT Class 12 Physics Chapter 5 (Magnetism and Matter), "Bar Magnet Magnetic Field" covers the core principles and equations students need for board exam success. The MyAiSchool lesson explains the topic with definitions, derivations, worked examples, and interactive simulations. Key formulas and dimensional analysis are included to build conceptual depth and problem-solving skills aligned with the CBSE 2025-26 syllabus.
How is Bar Magnet Magnetic Field useful in real-life applications?
Real-life applications of "Bar Magnet Magnetic Field" from NCERT Class 12 Physics Chapter 5 include electronics, communication systems, medical imaging, solar energy, semiconductor devices, and modern technology. The MyAiSchool lesson links every concept to a tangible example so students see physics as a problem-solving framework for the physical world, not as abstract formulas.
What are the key formulas in Bar Magnet Magnetic Field?
Key formulas in "Bar Magnet Magnetic Field" (NCERT Class 12 Physics Chapter 5 Magnetism and Matter) are derived step-by-step in the MyAiSchool lesson. Students should memorize the final formula AND understand its derivation for full board marks. Each formula is listed with its dimensional formula, SI unit, applicability range, and common pitfalls. The Summary section at the end of each part includes a quick-reference formula card.
How does this part connect to other parts of Chapter 5?
NCERT Class 12 Physics Chapter 5 (Magnetism and Matter) is structured so each part builds on the previous one. "Bar Magnet Magnetic Field" connects directly to neighbouring parts via shared definitions, units, and methodology. The MyAiSchool lesson cross-references related concepts with internal links so students can navigate the whole chapter as one connected story rather than disconnected fragments.
What types of CBSE board questions come from Bar Magnet Magnetic Field?
CBSE board questions from "Bar Magnet Magnetic Field" typically include: (1) 1-mark MCQs on definitions and formulas, (2) 2-mark short-answer derivations or applications, (3) 3-mark numerical problems with units, (4) 5-mark long-answer derivations followed by application. The MyAiSchool lesson tags each Competency-Based Question (CBQ) with Bloom level (L1-L6) so students know how to study for each weight.
How can students use the interactive simulation effectively?
The interactive simulation in the "Bar Magnet Magnetic Field" lesson allows students to adjust input parameters (sliders or selectors) and see physical quantities update in real time. To use it effectively: (1) try extreme values to understand limiting cases, (2) compare with the analytical formula, (3) check unit consistency, (4) test special configurations from worked examples. The simulation reinforces conceptual intuition that pure formula manipulation cannot.
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