Magnetism & Electromagnetism – NDA Physics Notes

Drop a paperclip near a magnet. It jumps.

That invisible pull (acting across empty space, through no visible mechanism) is magnetism. A permanent magnet needs no power supply, no circuit, no chemical reaction. It simply acts, continuously and silently, at a distance.

But magnetism and electricity are not separate phenomena. They are two aspects of one fundamental force: electromagnetism. Every current-carrying wire creates a magnetic field. Every changing magnetic field creates an electric current. These two relationships, discovered by Ørsted and Faraday respectively, power every generator, every motor, and every transformer in the modern world.

1. What Is Magnetism?

Magnetism is a force that acts between certain materials, attracting or repelling them across empty space without physical contact. Every magnet has two poles: a north pole (N) and a south pole (S). Like poles repel (N-N, S-S). Unlike poles attract (N-S). The force becomes weaker with distance.

Every magnet is a magnetic dipole. Both poles always exist together. Positive and negative electric charges can exist separately, but magnetic north and south poles always come as a pair. There are no magnetic monopoles: no isolated north or south pole can exist alone.

2. Magnetic Field Lines: Properties and Rules

Magnetic field lines (also called lines of force) visualise the magnetic field. They have very different properties from electric field lines.

Property 1: Always closed curves: Magnetic field lines form continuous closed loops. They never start or end anywhere. Unlike electric field lines (which begin on positive charges and terminate on negative charges), magnetic field lines have no starting or ending points because no magnetic monopoles exist. [NDA 2020-I & II]

Property 2: Never intersect: Two magnetic field lines can never cross each other. If two field lines intersected at a point, there would be two different directions of magnetic field at that single point, which is physically impossible. This holds everywhere: inside the magnet, at the poles, at neutral points, everywhere. [NDA 2010-I | NDA 2018-I | NDA 2020-I & II]

Property 3: Exist inside the magnet: Field lines run from the south pole to the north pole inside the magnet and from north to south outside. They are continuous closed loops passing through both the interior and exterior of the magnet. The incorrect statement is “there are no field lines within a bar magnet.” [NDA 2018-I]

Property 4: Cannot emanate from a single point: A field line appears to emerge from the north pole but actually continues in a closed loop through the interior of the magnet. Field lines cannot originate at any single point. [NDA 2018-I]

Property 5: Parallel and equally spaced in a uniform field: In a uniform magnetic field, field lines are parallel to each other and equally spaced, neither converging nor diverging. A converging pattern indicates a stronger field; a diverging pattern indicates a weaker field. [NDA 2011-I]

Property	Correct Statement	Incorrect (NDA Confusion)
Shape	Always closed curves (complete loops)	Open curves like electric field lines
Intersection	Never intersect anywhere	They intersect at poles or neutral points
Inside magnet	Exist inside: run S to N inside	No field lines inside a bar magnet
Origin/termination	Cannot start or end at any point	Emanate from north pole as a point source
In uniform field	Parallel and equally spaced	Convergent or divergent

3. Bar Magnets: Breaking, Demagnetisation, and Types

Breaking a Bar Magnet: Monopoles are Impossible

When a bar magnet is broken into two pieces, each piece becomes a complete magnet with its own north and south poles. Breaking never produces an isolated north pole or south pole. Even if a magnet is broken into a thousand tiny pieces, each piece will have both a north and a south pole. [NDA 2012-II]

Demagnetisation

Magnetism can be destroyed by: Heating to the Curie temperature (thermal energy overcomes domain alignment, causing domains to randomise and net magnetism to disappear) AND Rough handling (hammering) (physical shock disrupts domain alignment). [NDA 2010-II]

Keeping in the magnetic meridian or placing opposite to Earth’s horizontal intensity do NOT reliably demagnetise a magnet.

Types of Magnets

Type	Property	Duration
Artificial magnet	Manufactured magnets: require sustained influence to maintain magnetism	Short-lived without maintenance
Permanent magnet	Retains magnetism on its own indefinitely after being magnetised	Long period
Temporary magnet	Induced magnet: magnetic only while the inducing field is present	Only while field present
Earth as a magnet	Natural magnet: Earth’s magnetic field has persisted for billions of years	Essentially infinite

Matching: Artificial → short-lived. Permanent → long-lived. Temporary → induced. Earth → essentially infinite. [NDA 2012-II]

Identifying Poles of an Unmarked Magnet: The polarity of an unmarked horseshoe magnet is most reliably determined using a magnetic compass. The compass needle deflects and aligns with the field of the test magnet, identifying the poles. [NDA 2012-II]

4. Materials and Magnetism

Type	Examples	Behaviour in External Field	Relative Permeability	Strongly Attracted?
Ferromagnetic	Iron, Nickel, Cobalt and their alloys	Strongly attracted: magnetised in direction of field	Very large (hundreds to thousands)	YES: strongly
Paramagnetic	Aluminium, Platinum, Manganese	Weakly attracted: slight magnetisation in field direction	Slightly > 1	NO: very weakly
Diamagnetic	Bismuth, Copper, Water, most non-metals	Weakly repelled: slight magnetisation opposing field	Slightly < 1	NO: slightly repelled

NDA 2023-II: How many of these can be attracted by a magnet: Plastic (diamagnetic, no), Carbon (diamagnetic, no), Aluminium (very weakly paramagnetic: not significantly), Stainless Steel (austenitic stainless steel is non-magnetic). Answer: None strongly: effectively zero of the listed materials is strongly attracted. [NDA 2023-II]

5. Earth’s Magnetism

Magnetic Meridian

The magnetic meridian is an imaginary vertical plane passing through the magnetic north and south poles of Earth at any given location. [NDA 2015-II] Wrong answers to avoid: “a line along north-south” (it is a plane, not a line), “a horizontal plane” (it is a vertical plane).

Direction of Earth’s Field at Different Locations

At the magnetic equator: Earth’s field is purely horizontal. The dip angle is zero. [NDA 2017-I]

At the magnetic/geographical poles: Earth’s field is vertical. The dip angle is 90°.

Strength of Earth’s Magnetic Field

Earth’s magnetic field at the surface is approximately 1 Gauss = 10⁻⁴ Tesla. [NDA 2012-II] Values of 1 Tesla, 2 Gauss, or 10⁴ Tesla are all wrong by orders of magnitude.

6. Friction vs Magnetic Force: Contact vs Non-Contact

Friction force acts through physical contact between surfaces. It is a contact force. Magnetic force acts between magnets or between a magnet and a magnetic material without direct contact. It is a non-contact force. The statement “friction is a contact force while magnetic force is a non-contact force” is always true, regardless of temperature, surroundings, or other conditions. [NDA 2021-I]

7. Magnetic Effect of Electric Current

Hans Christian Ørsted discovered in 1820 that a current-carrying wire deflects a compass needle placed nearby. Every current-carrying wire creates a circular magnetic field around it. The field lines form complete circles centred on the wire. The direction of these circles depends on the direction of the current.

The direction of the magnetic field at a point due to a current-carrying wire is perpendicular to the plane containing both the wire and the point. [NDA 2010-II] It is not parallel or antiparallel to the current direction, and not along the perpendicular drawn from the wire to the point.

8. Right-Hand Thumb Rule: Straight Wire

To find the direction of the magnetic field around a current-carrying wire:

Grasp the wire with the right hand, with the thumb pointing in the direction of conventional current flow. The curled fingers point in the direction of the circular magnetic field lines around the wire.

★  IMPORTANT This is the ONLY rule: the Right-Hand Thumb Rule: and it applies for ALL directions of current. Upward, downward, toward the east, into the page, any direction. [NDA 2013-I | NDA 2021-II] Wrong: “Left-hand rule for upward current, right-hand rule for downward current.” There is only ONE rule.

9. Direction of Magnetic Field: Worked Problems

Problem Type 1: Current direction → Field direction:

Current downward into the page (⊗): Right-hand thumb rule with thumb pointing into the page: curled fingers move clockwise when viewed from the front. [NDA 2013-I]

Current upward out of the page (⊙): Right-hand thumb rule with thumb pointing out of the page: curled fingers move anti-clockwise when viewed from the front. [NDA 2013-I]

Problem Type 2: Field direction → Current direction: Anti-clockwise field lines seen when looking at a cross-section: the right-hand thumb rule tells us the thumb (current direction) must point out of the page = upward. [NDA 2021-II] If field circles clockwise: current is into the page (downward).

Problem Type 3: Field at a specific point: Horizontal power line carries current east-to-west. At a point directly below the wire: thumb pointing west (current), at the bottom of the circle the field points south to north. [NDA 2025-I]

The Strength of the Field

B = μ₀I / (2πr)

B depends directly on current I and inversely on distance r. [NDA 2018-II | NDA 2022-I] At greater distance from the wire, B decreases (B ∝ 1/r). B does not depend on the radius of the wire, temperature, or any other factor.

10. Force on a Moving Charge in a Magnetic Field

When a charged particle moves through a magnetic field, it experiences a force always perpendicular to both the particle’s velocity and the magnetic field.

F = q(v × B) = qvB sinθ

F = force (N). q = charge (C). v = speed (m s⁻¹). B = magnetic field (T). θ = angle between velocity v and field B.

★  IMPORTANT When a charged particle moves parallel (or antiparallel) to the magnetic field (θ = 0° or 180°): sin0° = sin180° = 0   →   F = 0   →   No force → particle continues unchanged. [NDA 2015-I | NDA 2023-I] Wrong answers: “traces a helical path,” “traces a circular path,” “comes to rest.” All require a non-zero force.

Positive vs Negative Charges Separate: When a mixture of positive and negative charges moves through a perpendicular magnetic field, F = qv × B gives opposite directions for opposite signs. The two types of charges are deflected in opposite directions and separate spatially. [NDA 2023-II]

Worked Direction Problem: A positively charged particle projected west is deflected north. Using F = q(v × B): v points west, F points north. Since west × up = north (right-hand rule), B points vertically upward. [NDA 2013-I]

Zero Force: Antiparallel: A positive charge moving southward in a northward magnetic field: these are antiparallel. v × B = 0. Force = zero. No deflection. [NDA 2023-I]

11. Fleming’s Left-Hand Rule: Force on Current-Carrying Conductor

When a current-carrying conductor is placed in a magnetic field, it experiences a force. The direction of this force is given by Fleming’s Left-Hand Rule (the motor rule). Stretch the thumb, forefinger, and middle finger of the left hand so they are mutually perpendicular:

Forefinger → direction of magnetic field (B)

Middle finger → direction of current (I)

Thumb → direction of force (motion) on conductor

Fleming’s Left-Hand Rule applies to motors, which are devices that convert electrical energy to mechanical motion. [NDA 2025-II]

12. Torque on a Current-Carrying Coil

A rectangular coil carrying current, placed in a magnetic field, experiences a torque (a turning effect) that tends to align the coil with the field.

τ = NBIA sinθ

τ = torque (N m). N = number of turns. B = magnetic field strength (T). I = current (A). A = area of coil (m²). θ = angle between the coil plane and the magnetic field direction.

★  IMPORTANT Torque is MAXIMUM when the coil PLANE is PARALLEL to the magnetic field (θ = 90°, sinθ = 1). Torque is ZERO when the coil plane is PERPENDICULAR to the field (θ = 0°, sin0° = 0). [NDA 2012-I]: The most commonly tested misconception in this chapter.

Factor	Effect on Torque	From Formula τ = NBIA sinθ
More turns (N ↑)	Torque increases: N is directly proportional	τ ∝ N
Stronger field (B ↑)	Torque increases	τ ∝ B
Larger current (I ↑)	Torque increases	τ ∝ I
Larger area (A ↑)	Torque increases	τ ∝ A
Fewer turns (N ↓)	Torque decreases	τ ∝ N
Coil perpendicular to field	Torque = ZERO	sin0° = 0

13. Solenoid: Formula, Uniformity, and Dependence

A solenoid is a long cylindrical coil of wire wound in a helix. When current flows through it, it produces a strong, nearly uniform magnetic field inside, similar to that of a bar magnet.

B = μ₀nI

B = magnetic field inside (T). μ₀ = 4π × 10⁻⁷ T m A⁻¹. n = turns per unit length (m⁻¹). I = current (A).

Factor	Does B Inside Solenoid Depend On It?	Reason
Turns per unit length (n)	YES: B ∝ n	More turns per length = more overlapping magnetic fields
Current (I)	YES: B ∝ I	More current = stronger field from each turn
Diameter of solenoid	NO	Diameter does not appear in B = μ₀nI
Total length (at same n)	NO (B unchanged)	n = turns/length; if both change proportionally, n stays same
Core material (μ_r)	YES: B → μ_r × μ₀nI	Core with high permeability amplifies field

NDA 2019-I: B depends on n (YES) and I (YES) but NOT on diameter. Answer: 1 and 2 only. [NDA 2019-I]

NDA 2017-I: turns per unit length doubled (n → 2n), current unchanged: B_new = μ₀(2n)I = 2B. [NDA 2017-I]

Field Inside Is Uniform: The magnetic field inside a long solenoid is uniform, the same everywhere inside. [NDA 2025-I | NDA 2025-II] A solenoid carrying current behaves like a bar magnet. One end acts as a north pole and the other as a south pole. [NDA 2022-II]

14. Circular Coil: Magnetic Field at Centre

A circular loop of wire carrying current produces a magnetic field. At the centre of the coil:

B = μ₀NI / (2R)

N = number of turns. I = current (A). R = radius of the coil (m).

Worked Example: Circular coil of radius R, N turns, current I gives B = 0.1 T at the centre. If N → 2N and R → R/2: B_new = μ₀(2N)I / (2 × R/2) = μ₀(2N)I / R = 4 × μ₀NI/(2R) = 4 × 0.1 = 0.4 T. [NDA 2018-II] Doubling N and halving R both increase B. The combined effect is 4×.

15. Electromagnets: Soft Iron Core in Solenoid

When a soft iron core is inserted inside a solenoid, the magnetic field inside increases dramatically, by a factor equal to the relative permeability (μ_r) of the iron, which can be hundreds to thousands.

B_with_core = μ_r × B_without_core

The incorrect statement: “if a soft iron bar is inserted inside the solenoid, the magnetic field remains the same.” This is false. The field increases substantially. [NDA 2022-II] Soft iron’s high permeability is the operating principle of electromagnets used in cranes, bells, and MRI machines.

Why soft iron (not hard steel)? Soft iron is easily magnetised and easily demagnetised, ideal for electromagnets that need to be switched on and off. Hard steel retains its magnetism and is used for permanent magnets.

16. Detecting Magnetic Fields

The presence (and direction) of a magnetic field at a location is detected using a magnetic needle (compass). [NDA 2022-II] An ammeter measures current. A voltmeter measures voltage. A motor converts electrical to mechanical energy. None of these can detect the presence or direction of a magnetic field the way a compass does.

MRI: Magnetic Resonance Imaging: MRI works by applying a powerful external magnetic field (generated by the MRI machine) to the body. This field causes hydrogen nuclei (protons) in body tissues to align and precess, producing detectable radio-frequency signals. [NDA 2013-I]

17. Household Appliances and Magnets

Calling bell: A solenoid (electromagnet) attracts a metal strip that strikes the bell repeatedly.

Electric fan: An electric motor drives the fan. Every motor contains electromagnets or permanent magnets.

Washing machine: Also driven by an electric motor: which contains magnets.

All three are correct answers: calling bell, electric fan, and washing machine all use magnets. [NDA 2012-I]

18. Electromagnetic Induction: Faraday’s Law

In 1831, Michael Faraday discovered that a changing magnetic flux through a coil induces an EMF in the coil. This is electromagnetic induction (EMI).

What Causes an Induced EMF

Electromagnetic induction produces an induced current in a coil when the magnetic flux through it changes. The change can be caused by: moving a magnet toward or away from the coil, changing the current in a nearby coil (mutual inductance), rotating the coil in a magnetic field (generator), or changing the area of the coil in a magnetic field.

EMI is caused by changing magnetic flux: not by a changing electric field. [NDA 2014-I]

Faraday’s Law (Quantitative)

The induced EMF is equal to the rate of change of magnetic flux:

ε = −dΦ/dt

ε = induced EMF (V). Φ = magnetic flux = BA cosθ (Weber). t = time (s). The negative sign comes from Lenz’s Law. Magnetic flux Φ = B × A × cosθ. B = field strength (T). A = area (m²). θ = angle between B and the normal to the coil plane.

19. Lenz’s Law

The direction of the induced current is such that it opposes the change in magnetic flux that caused it.

If a north pole approaches a coil from the left, the induced current flows in a direction that creates a north pole on the left face of the coil: pushing back against the approaching magnet. This is an application of conservation of energy. If the induced current aided the change, energy would be created from nothing.

Applications of Lenz’s Law

Eddy currents: When a conducting plate moves through a magnetic field, induced currents (eddy currents) flow in closed loops within the plate. By Lenz’s Law, they oppose the motion, creating a braking effect. Applications: electromagnetic braking, induction cookers, electric meters (damping).

Self-inductance: When the current in a coil changes, it changes the flux through itself, inducing a back-EMF that opposes the change in current. This is self-induction.

20. Fleming’s Right-Hand Rule: Generator Action

When a conductor moves through a magnetic field, the induced current direction is given by Fleming’s Right-Hand Rule (the generator rule). Stretch the thumb, forefinger, and middle finger of the right hand so they are mutually perpendicular:

Forefinger → direction of magnetic field (B)

Thumb → direction of motion of conductor

Middle finger → direction of induced current   [NDA 2022-I]

Rule	Hand Used	Forefinger	Middle Finger	Thumb	Application
Fleming’s Left-Hand Rule	Left	Magnetic Field (B)	Current (I)	Force on conductor (motion)	Motor: electrical to mechanical
Fleming’s Right-Hand Rule	Right	Magnetic Field (B)	Induced Current	Motion of conductor	Generator: mechanical to electrical

Memory aid: “L-M: Left hand for Motor. R-G: Right hand for Generator.” Match the first letters.

Hund’s Rule: Completely Different: Hund’s Rule applies to electron filling in atomic orbitals: unrelated to electromagnetism. When asked which rule applies to force on a current-carrying conductor in a magnetic field: the answer is Fleming’s Left-Hand Rule, not Hund’s Rule. [NDA 2025-II]

21. Self-Inductance and Mutual Inductance

Self-Inductance

When the current in a coil changes, the changing magnetic flux through the coil induces a back-EMF that opposes the change:

e = −L (dI/dt)

L = coefficient of self-inductance (measured in Henry, H). [NDA 2017-II] dI/dt = rate of change of current. The SI unit of inductance is the henry (H), named after Joseph Henry. It is not “Holm,” “Halogen,” or “Hertz” (Hertz is the unit of frequency). 1 H = 1 V·s/A = 1 Ω·s. [NDA 2017-II]

Mutual Inductance

When the current in one coil (primary) changes, the changing flux links with a neighbouring coil (secondary), inducing an EMF in it. This is mutual inductance, the principle behind transformers.

22. AC and DC Generators

Both AC and DC generators work on Faraday’s laws of electromagnetic induction. A rotating coil in a magnetic field generates an induced EMF. [NDA 2022-II] The difference is entirely in the output circuit:

Feature	AC Generator	DC Generator
Principle	Faraday’s laws of EMI	Faraday’s laws of EMI (same)
Output collector	Slip rings and brushes	Split-ring commutator
Why different output	Slip rings maintain continuous connection: alternating internal EMF → alternating output	Commutator reverses connections every half-rotation: alternating internal EMF → unidirectional (DC) output
Output type	Sinusoidal alternating current	Pulsating (rectified) direct current
Conversion	To convert AC to DC generator: replace slip rings with commutator	To convert DC to AC generator: replace commutator with slip rings

To convert an AC generator to a DC generator: replace slip rings with a split-ring commutator. [NDA 2023-II] Generator converts mechanical energy to electrical energy. Motor converts electrical energy to mechanical energy.

23. Transformers

A transformer changes AC voltage levels. It cannot work on DC. [NDA 2017-I | NDA 2017-II] A transformer works on the principle of mutual induction. The changing current in the primary coil creates a changing flux that induces an EMF in the secondary coil.

Transformer Equation

V₁/V₂ = N₁/N₂ = I₂/I₁

Type	Turns Ratio	Voltage	Current	Application
Step-up transformer	N₂ > N₁	V₂ > V₁ (increased)	I₂ < I₁ (decreased)	Power station to transmission lines
Step-down transformer	N₂ < N₁	V₂ < V₁ (decreased)	I₂ > I₁ (increased)	Transmission lines to homes/factories

Step-up transformer increases voltage (and decreases current). [NDA 2017-II] The device that changes low AC voltage to high AC voltage is a transformer, not a generator, motor, or vibrator. [NDA 2017-I] An ideal transformer is 100% efficient: V₁I₁ = V₂I₂.

24. AC Circuits: Reactance and Impedance

Inductive Reactance

X_L = ωL = 2πfL   (Ohm, Ω)

An inductor opposes changes in current. Its opposition to AC current increases with frequency. Higher frequency gives higher X_L.

Capacitive Reactance

X_C = 1/(ωC) = 1/(2πfC)   (Ohm, Ω)

A capacitor’s opposition decreases with frequency. Higher frequency gives lower X_C, so the capacitor passes high-frequency AC more easily.

Impedance of LCR Circuit

Z = √(R² + (X_L − X_C)²)   (Ohm, Ω)

Resonance: When X_L = X_C

At resonance, X_L = X_C, so Z = R (minimum impedance). Current is maximum. Resonant frequency:

ω₀ = 1/√(LC)   or   f₀ = 1/(2π√(LC))

Application: Radio tuning circuits select a specific frequency (station) by setting the LC circuit to resonate at that frequency.

25. Cyclotron

A cyclotron is a particle accelerator that uses a magnetic field to bend charged particles into a circular path and an alternating electric field to accelerate them in a spiral. The magnetic force on a charged particle moving perpendicular to the field is centripetal: qvB = mv²/r → r = mv/(qB). As the particle accelerates, v increases, so r increases. The path spirals outward.

Key property: The time period T = 2πm/(qB) is independent of speed, allowing the accelerating electric field to always be applied at the right phase. This is the cyclotron resonance condition. Applications: producing radioactive isotopes for medical imaging, cancer treatment, fundamental particle physics research.

26. Magnetic Materials: Para, Dia, Ferromagnetic

Ferromagnetic Materials

Strongly attracted by magnets. Large magnetic domains align with external field. Examples: iron, nickel, cobalt, and their alloys. Relative permeability μ_r >> 1 (hundreds to thousands). Above the Curie temperature, ferromagnetic materials become paramagnetic. Domains disorder.

Paramagnetic Materials

Weakly attracted by magnets. Individual atoms have magnetic moments but no domain structure. Moments only partially align in an external field. Examples: aluminium, platinum, manganese. μ_r slightly > 1.

Diamagnetic Materials

Weakly repelled by magnets. No permanent magnetic moments: a magnetic moment is induced opposing the applied field. Examples: bismuth, copper, silver, water, most non-metals, wood. μ_r slightly < 1. Superconductors are perfect diamagnets below their critical temperature. They completely expel magnetic fields (Meissner effect).

Important Distinctions

Magnetic Field Lines vs Electric Field Lines

Electric field lines: start on positive charges, end on negative charges. They are open curves. Magnetic field lines: always closed loops, with no starting or ending points (no monopoles exist). The most fundamental difference in how the two fields are visualised.

Fleming’s Left-Hand Rule vs Right-Hand Rule

Left-Hand Rule (Motor rule): force on a current-carrying conductor in a field. Right-Hand Rule (Generator rule): direction of induced current in a moving conductor. Left = Motor. Right = Generator.

Solenoid B: What Matters and What Doesn’t

B = μ₀nI. Matters: n (turns per length) and I (current). Does NOT matter: diameter of solenoid, total length (if n stays same), cross-sectional shape. Core material (if changed to iron): multiplies B by μ_r.

AC Generator vs DC Generator

Same principle (Faraday’s law). Same internal operation (rotating coil in field). Different output collection: slip rings → alternating output (AC). Split-ring commutator → rectified output (DC).

Transformer: Only AC

A transformer requires changing magnetic flux (dΦ/dt ≠ 0) to induce an EMF. DC produces constant flux → no change → no induced EMF → transformer does not work on DC. AC is essential.

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