Magnetism & Matter And Electromagnetic Induction: Key Concepts, Formulas, Tricks For NEET 2026

Magnetism and Matter explains how bar magnets behave and how magnetic fields arise around them. It covers the magnetic dipole moment, torque, potential energy and oscillations of a magnet in a uniform field, and how diamagnetic, paramagnetic and ferromagnetic materials respond to an external field.

Electromagnetic Induction explains how a changing magnetic flux produces emf and current. It builds on Faraday’s law and Lenz’s law to explain motional emf, self and mutual inductance, RL circuits and the AC generator.

NEET questions from these chapters often test direction rules, proportionality, field comparisons, cutting or bending of magnets, Lenz’s law and standard induction formulas. A clear grasp of these concepts helps you solve questions quickly and accurately.

Bar Magnet And Magnetic Dipole Moment

A bar magnet has two poles:

• North pole

• South pole

The magnetic dipole moment is a vector quantity directed from the South Pole To The North Pole.

For a bar magnet:

M = m l

where m is pole strength and l is the magnetic length.

For a current-carrying coil:

M = I A

where I is current and A is the coil area.

The SI unit of magnetic dipole moment is A m².

Pole Strength

Pole strength is a scalar quantity:

m = M / l

Its SI unit is A m.

Pole strength depends on cross-sectional area:

m proportional to A

Since magnetic moment is M = m l, it follows that:

M proportional to A l

Therefore:

M proportional to Volume

Addition Of Magnetic Dipole Moments

Magnetic dipole moment follows vector addition. For two equal moments M:

The angle between two magnetic moments must be measured using their vector directions, not directly from the physical lengths of the bar magnets.

First identify the South-to-North direction of each magnet. A physical angle between magnets may represent a different angle between their magnetic moments.

Cutting And Bending Of A Bar Magnet

A bar magnet is the simplest source of a magnetic field, with two opposite poles at its ends. Its strength and orientation are described by the magnetic dipole moment, which is the key quantity in most NEET problems on magnets.

Cutting Along The Length

When a magnet is cut along its length into n equal parts:

• Length remains unchanged.

• Cross-sectional area becomes 1/n.

• Pole strength becomes m/n.

• Magnetic moment becomes M/n.

Thus:

m' = m/n

M' = M/n

Cutting Perpendicular To The Length

When the magnet is cut perpendicular to its length:

• Cross-sectional area remains unchanged.

• Length becomes l/n.

• Pole strength remains unchanged.

• Magnetic moment becomes M/n.

Bending Into A Circular Arc

If a magnet of moment M is bent into an arc subtending angle theta at the centre:

M' = M [sin(theta/2) / (theta/2)]

Here, theta must be expressed in radians.

For a half-ring:

M' = 2M / pi

Bending reduces the magnetic moment because the effective separation between the poles decreases.

Bending At The Midpoint

If the two arms make an angle theta:

M' = M sin(theta/2)

For arms at 60 degrees:

M' = M/2

Magnetic Field Of A Bar Magnet

For a short magnetic dipole at distance r:

Axial Field

B axial = 2 k M / r³

The field is along the magnetic moment.

Equatorial Field

B equatorial = k M / r³

The field is opposite to the magnetic moment.

Therefore, at equal distances:

B axial = 2 B equatorial

At a general point making angle theta with the magnetic moment:

B = k M / r³ × square root of (1 + 3 cos² theta)

The field direction is also important:

tan alpha = tan theta / 2

where alpha is the angle made by the field with the radial direction.

Torque, Energy And Oscillation

A magnetic dipole in a uniform magnetic field experiences zero net force but may experience torque.

Torque

tau = M B sin theta

Torque is maximum at 90 degrees and zero at 0 degrees and 180 degrees.

Potential Energy

U = - M B cos theta

• At 0 degrees: energy is minimum, and equilibrium is stable.

• At 180 degrees: energy is maximum, and equilibrium is unstable.

• At 90 degrees: energy is zero.

The time period of small oscillations is:

T = 2 pi square root of (I / M B)

where I is the moment of inertia.

If a magnet is cut along its length, both I and M reduce in the same ratio, so the time period remains unchanged. If it is cut perpendicular to its length into n parts, the time period becomes T/n.

Magnetic Materials And Hysteresis

Magnetic materials are classified by their response to an external magnetic field.

Magnetic susceptibility is:

chi = Magnetisation / H

It is dimensionless. The important relation is:

mu r = 1 + chi

For paramagnetic materials:

chi proportional to 1/T

Ferromagnetic materials contain magnetic domains. Above the Curie temperature, they become paramagnetic.

Hysteresis

Hysteresis is the lag of magnetisation behind the applied magnetic field.

• Hard magnetic materials have high retentivity and coercivity. They are used for permanent magnets.

• Soft magnetic materials have low retentivity and coercivity. They are used in electromagnets and have lower energy loss.

The area of the hysteresis loop represents energy loss.

Magnetic Flux

Magnetic flux is:

Phi = B A cos theta

The angle is measured between the magnetic field and the area vector, not the plane.

• Field perpendicular to the plane: flux is maximum, Phi = B A.

• Field parallel to the plane: flux is zero.

• SI unit: weber.

For a closed surface, net magnetic flux is zero because magnetic field lines form closed loops.

Lenz’s Law And Faraday’s Law

Lenz’s Law states that the induced current opposes the change in magnetic flux.

• Increasing outward field produces an inward induced field.

• Decreasing outward field produces an outward induced field.

• Constant flux produces no induced current.

Faraday’s law is:

emf = - d Phi / dt

For a coil with N turns:

emf = - N d Phi / dt

The negative sign represents Lenz’s law.

A loop entering a magnetic-field region has induced current. A loop completely inside a uniform field has no induced current because flux is constant. A loop leaving the region again has induced current in the opposite direction.

Motional And Rotational EMF

For a conducting rod of length l moving with speed v perpendicular to magnetic field B:

emf = B v l

If circuit resistance is R:

I = B v l / R

The magnetic force opposing motion is:

F = B² l² v / R

For constant velocity, an equal external force is required.

If any two of the rod length, velocity and magnetic field are parallel, motional emf is zero.

For a rotating rod of length L:

emf = 1/2 B omega L²

Use the effective length measured from the axis of rotation.

Self-Inductance, Mutual Inductance And RL Circuits

Self-inductance produces back emf:

emf = - L dI / dt

Energy stored in an inductor is:

U = 1/2 L I²

For a long solenoid:

L = mu naught N² A / l

At the instant of switching:

• An inductor behaves as an open circuit.

• At steady state, it behaves as a wire.

For uncoupled inductors:

• Series: L equivalent = L1 + L2

• Parallel: L equivalent = L1 L2 / (L1 + L2)

Mutual inductance is:

M = k square root of (L1 L2)

For series-connected coupled inductors:

L equivalent = L1 + L2 plus or minus 2M

The sign depends on whether mutual fluxes support or oppose each other.

AC Generator And Eddy Currents

For a rotating coil:

emf = N B A omega sin(omega t)

Maximum emf is:

emf maximum = N B A omega

Maximum current is:

I maximum = N B A omega / R

Eddy currents are circulating currents induced in conducting materials by changing magnetic flux. They are used in magnetic brakes, induction furnaces, speedometers and electrical instruments.

Exam Tips For Magnetism And Electromagnetic Induction

Most NEET questions from these two chapters test direction rules, quick proportionality and standard formulas rather than long derivations. Keep these points in mind while revising and solving questions.

• Directions first: Always take the dipole moment from South to North, and find the area vector before calculating flux. Most wrong answers come from direction errors, not formulas.

• Cutting and bending: The magnetic moment always decreases. Cutting along the length gives M/n with the same period, and cutting perpendicular gives M/n with period T/n. For bending, use sin(θ/2)/(θ/2) for an arc and sin(θ/2) for a midpoint bend.

• Field comparisons: B axial = 2 × B equatorial. For perpendicular points, add the fields as vectors, not as plain numbers.

• Equilibrium: θ = 0° is stable (minimum energy), and θ = 180° is unstable (maximum energy). Torque is maximum at 90°.

• Inductor circuits: At t = 0, the inductor is an open circuit, and at steady state it is a wire. Draw the equivalent circuit before solving.

• Motional emf: Check that B, v and l are mutually perpendicular. For a rotating rod, use the effective length in ½BωL².

• Common traps: Diamagnetic χ is negative, ferromagnets turn paramagnetic above the Curie temperature, and the area of the hysteresis loop equals energy loss.

Magnetism & Matter and Electromagnetic Induction rest on a few core ideas: dipole moment (cutting, bending, torque, oscillations), the behaviour of magnetic materials, and Faraday’s and Lenz’s laws leading into inductance and the AC generator. Mastering these formulas and their direction rules covers most NEET questions from both chapters.

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