Magnetism and Matter

Magnetism and MatterNEET Physics · Class 12 · NCERT Chapter 5

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7 interactive concept widgets for Magnetism and Matter. Drag any slider, change any number, and watch the formula and the answer update live. Built so you understand how each NEET problem actually works, not just the final number.

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Field of a bar magnet

Torque on a bar magnet

Earth's magnetic elements

Susceptibility classifier

Material types

Curie's law for paramagnets

Hysteresis loop

Bar magnet and Earth's field

Field of a bar magnet, torque it feels in an external field, and the elements of Earth's magnetism.

Bar magnet

Field of a bar magnet (axial vs equatorial)

The magnetic dipole results, twin to the electric dipole.

Field of a bar magnet at distance r (much larger than its length). Axial = 2x equatorial.

Moment m: 2.00 A·m²

Distance r: 10.0 cm

Field B

400.00 µT

B = \frac{2 μ _{0} m}{4 π r ^{3}}

Try this

For the same r, axial field is twice the equatorial field.
Both fall as 1/r³ (faster than a single charge).
Direction: axial along m. Equatorial opposite to m.

Torque

Torque on a bar magnet

Same form as the electric dipole result.

Torque on a bar magnet in a uniform external field. Tries to align m with B.

m: 0.50 A·m²

B: 50.0 mT

θ: 60°

Torque τ

2.17e-2 N·m

τ = m B sin θ

Potential energy U

-1.25e-2 J

U = - m \cdot B = - m B cos θ

Try this

θ = 0°: stable equilibrium. τ = 0, U is minimum.
θ = 90°: maximum torque, U = 0.
θ = 180°: unstable. τ = 0 but the slightest nudge flips the magnet.

Earth's field

Earth's magnetic elements

Horizontal component, dip angle and the resulting total field.

Earth's magnetic field at a place is described by horizontal component B_H and dip angle. The total field and vertical component follow.

B_H (horizontal): 0.400 G

Dip angle δ: 60°

Total field B

0.800 G

= 80.0 µT

B = B_{H} / cos δ

Vertical component B_V

0.693 G

B_{V} = B_{H} tan δ

Try this

At magnetic equator: dip = 0°, total field = B_H, no vertical component.
At magnetic poles: dip = 90°, B_H = 0, all the field is vertical.
In Delhi: B_H ≈ 0.35 G, dip ≈ 42°, total B ≈ 0.47 G.

Magnetic materials

Classify materials, see Curie's law for paramagnets, and explore the hysteresis loop of a ferromagnet.

Susceptibility

Magnetic susceptibility classifier

χ tells you whether a material is dia-, para- or ferro-magnetic.

Magnetic susceptibility chi: M = chi H. Sign and size of chi tell you the type of material.

χ (susceptibility)

Try -0.0001 (diamagnetic), 0.001 (paramagnetic), 1000 (ferromagnetic).

Relative permeability μ_r

1.001e+0

μ_{r} = 1 + χ

Material type

paramagnetic

Try this

Diamagnetic (Bi, Cu, water, Hg): χ ≈ -10⁻⁵. μ_r slightly < 1.
Paramagnetic (Al, O₂, Pt): χ ≈ +10⁻⁴. μ_r slightly > 1.
Ferromagnetic (Fe, Ni, Co): χ from 10² to 10⁵. μ_r much greater than 1.

Materials

Magnetic material classifier

Compare diamagnetic, paramagnetic and ferromagnetic substances at a glance.

Three classes of magnetic substances. Pick one to see its properties.

Diamagnetic

χ: small negative (~ -10⁻⁵)

μ_r: slightly < 1

Alignment: opposes B (weakly)

T dependence: no T dependence

Examples: Bi, Cu, Hg, water, gold, NaCl

M = χH, B = μ_{0} (H + M), μ_{r} = 1 + χ

Try this

Diamagnetism is universal but usually masked by stronger para- or ferro-magnetism if present.
A paramagnetic substance becomes diamagnetic in superconducting state (perfect diamagnetism, Meissner effect).
A ferromagnetic material above its Curie temperature behaves as a paramagnet (Curie-Weiss law).

Curie's law

Curie's law for paramagnets

Susceptibility falls as 1/T. Heating disorders the dipole moments.

For a paramagnet, susceptibility chi = C / T (Curie's law). Heating reduces alignment, dropping chi.

Curie constant C: 0.050 K

Applied field H: 1000 A/m

χ at 300 K = 1.67e-4

M at 300 K = 1.67e-1 A/m

χ = \frac{C}{T}, M = χH

Try this

Doubling T halves chi (1/T law).
For a ferromagnet ABOVE the Curie point T_C, behaviour is paramagnetic and Curie law applies.
Below T_C, ferromagnets follow the Curie-Weiss law: chi = C/(T - T_C).

Hysteresis

Hysteresis loop

The M vs H signature of a ferromagnetic material.

M vs H curve for a ferromagnetic material. The loop encloses energy lost as heat per cycle.

Coercivity (width): 40

Retentivity (height): 60

Wide loop = HARD magnet (high coercivity). Stays magnetised. Used in permanent magnets.

Narrow loop = SOFT magnet (low coercivity). Easy to magnetise/demagnetise. Used in transformer cores.

Try this

Retentivity = M when H = 0 after saturation. The leftover magnetism.
Coercivity = reverse H needed to bring M back to 0.
Loop area = energy dissipated per cycle (heat). Soft magnets minimise this for transformers.

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Moving Charges and Magnetism

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