MHT-CET Physics · Formula sheet

Magnetic Materials formulas

4 formulas, 2 reference tables and 12 common traps for MHT-CET Physics Magnetic Materials, grouped by subtopic.

Magnetic Dipole Moment

Moment, Torque, Work and Oscillation

Magnet in a field

\tau = MB\sin\theta, \qquad W = MB(1 - \cos\theta), \qquad T = 2\pi\sqrt{\frac{I}{MB}}

The Orbiting Electron's Moment

Orbital moment

\mu = \frac{e}{2m}L, \qquad \mu_B = \frac{eh}{4\pi m}

Common traps

Keeping the length when a rod is bent

The moment uses the straight distance between the poles. A rod bent into a semicircle has its poles a diameter 2L/π apart, not L.

Subtracting moments of magnets held with like poles together

Like poles together, the magnets point the same way and the moments ADD: 2M and M give 3M, so the period is SHORTER. Unlike poles together, they subtract to M.

Writing the gyromagnetic ratio as e/m

The loop's area and current give μ/L = e/2m — half of e/m.

Dropping the minus sign

The electron is negative, so its orbital moment points OPPOSITE its angular momentum: μ = −(e/2m)L.

Magnetisation, Susceptibility and Permeability

Learn this subtopic in the notes

B, H, M, χ and μ

Field in a material

B = \mu_0(H + M) = \mu_0(1 + \chi)H, \qquad \mu_r = 1 + \chi

Computing a Magnetisation

Magnetisation

M = \frac{m}{V} = (\mu_r - 1)\,nI

Common traps

Taking μᵣ = χ

μᵣ = 1 + χ. For iron with χ = 5499, μᵣ = 5500; the option 5499 is the trap.

Quoting (1 + χ) as the percentage rise

A toroid filled with a material of susceptibility χ has B multiplied by (1 + χ), so the RISE is χ × 100%.

Leaving cm² and cm in the volume

4 cm × 2 cm² is 8 × 10⁻⁶ m³. Mixed units put the answer off by powers of ten, and the options are spaced that way.

Using μᵣ where μᵣ − 1 belongs

M = (μᵣ − 1)nI. With μᵣ = 5000 the difference is negligible, but with a weakly magnetic core, using μᵣ counts the vacuum part of the field as magnetisation.

Dia-, Para- and Ferromagnets, Hysteresis and Shielding

Learn this subtopic in the notes

The Three Classes and Curie's Law

Class	Susceptibility	Temperature
Diamagnetic	Small, negative	Independent of T
Paramagnetic	Small, positive	χ = C/T (Curie's law)
Ferromagnetic	Very large, positive	Becomes paramagnetic above the Curie temperature

Hysteresis, Electromagnets and Shielding

Use	Retentivity	Coercivity
Electromagnet core (soft iron)	High	Low
Permanent magnet (steel, alnico)	High	High
Magnetic shield	—	Soft ferromagnet, high permeability

Common traps

Letting a diamagnet's χ change with temperature

Diamagnetism comes from induced orbital moments and does not depend on temperature; the χ–T graph is a flat line below zero. Only paramagnets follow Curie's law.

Writing Curie's law upside down

Magnetisation grows with the applied field and falls with temperature: M = CB/T, so C = MT/B.

Swapping retentivity and coercivity on the loop

Retentivity is where the loop crosses the B-axis (H = 0); coercivity where it crosses the H-axis (B = 0).

Shielding with a diamagnet

A diamagnet repels field lines only weakly. Shielding needs a soft ferromagnet, whose high permeability carries the field around the protected space.

Magnetic Materials formulas

Magnetic Dipole Moment

Moment, Torque, Work and Oscillation

The Orbiting Electron's Moment

Common traps

Magnetisation, Susceptibility and Permeability

B, H, M, χ and μ

Computing a Magnetisation

Common traps

Dia-, Para- and Ferromagnets, Hysteresis and Shielding

The Three Classes and Curie's Law

Hysteresis, Electromagnets and Shielding

Common traps

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