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medium difficulty11 min

Magnetisation, Magnetic Intensity and Susceptibility

Magnetisation M is the magnetic dipole moment per unit volume of a material. Magnetic intensity H represents the magnetising field, and magnetic susceptibility chi measures how strongly a material becomes magnetised in response to H.

In one line: M is material response, H is applied magnetising field, chi tells how responsive the material is.

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Understand it

  • When a material is placed in a magnetic field, its atomic or molecular magnetic dipoles respond to the field.
  • The net magnetic dipole moment per unit volume is called magnetisation M.
  • Magnetic intensity H is used to describe the applied magnetising effect, while the magnetic field inside the material is related to both H and M by B = μ0(H + M).
  • For a linear magnetic material, susceptibility is chi = M/H, so the sign and magnitude of chi tell whether the material is weakly repelled, weakly attracted, or strongly attracted by a magnetic field.

Example

If a material has M = 120 A m−1 when H = 400 A m−1, then chi = M/H = 120/400 = 0.30. The positive value indicates that magnetisation is in the same direction as the magnetising field.

Formula and rule

Key formulas: M = mnet/V, where M is magnetisation in A m−1, mnet is net magnetic dipole moment in A m2, and V is volume in m3.

B = μ0(H + M), where B is magnetic field in tesla, μ0 is permeability of free space, and H and M are in A m−1. chi = M/H for linear materials, where chi is dimensionless.

Use these relations for material-response questions under ordinary school-level linear assumptions unless non-linear ferromagnetic behaviour is specifically mentioned.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A sample of volume 2.0 × 10−5 m3 has net magnetic dipole moment 6.0 × 10−3 A m2 in an applied magnetic intensity of 1.5 × 103 A m−1.

  1. 1Find M and chi.
  2. 2Calculation: M = mnet/V = (6.0 × 10−3)/(2.0 × 10−5) = 3.0 × 102 A m−1. chi = M/H = (3.0 × 102)/(1.5 × 103) = 0.20.
  3. 3Interpretation: the positive susceptibility means the magnetisation is along the applied field.

Method you can reuse

For problems: identify whether M, H, B, chi, volume, or dipole moment is given; choose M = mnet/V, chi = M/H, or B = μ0(H + M); keep M and H in A m−1; check whether chi should have a unit; state what the sign of chi implies.

Visual tip

A conceptual diagram may show a material specimen in an applied magnetic field H, with small dipoles partly aligned, producing magnetisation M. For formula questions, a diagram is helpful but not essential.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is magnetic susceptibility dimensionless?

Think first, then show answer
Magnetic susceptibility is dimensionless because chi = M/H, and both magnetisation M and magnetic intensity H have the same SI unit, A m−1. Their units cancel in the ratio.

Common wrong answer

Writing susceptibility in A m−1 is wrong. Susceptibility has no unit because it is the ratio of M to H.

Don't mix this up

Students often treat B, H, and M as the same quantity. They are related but not identical, and their SI units are different.

Exam tip

For direct formula questions, write B = μ0(H + M) and chi = M/H clearly. Mention that chi is dimensionless because M and H have the same SI unit.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

This is commonly tested through definitions, unit-based questions, formula substitution, and comparison questions where susceptibility is used to classify magnetic materials.
  1. 1

    Enough for 1 mark

    Magnetisation M is the magnetic dipole moment per unit volume of a material. Magnetic intensity H represents the magnetising field, and magnetic susceptibility chi measures how strongly a material becomes magnetised in response to H.

  2. 2

    Add for 2 marks

    Example: If a material has M = 120 A m−1 when H = 400 A m−1, then chi = M/H = 120/400 = 0.30. The positive value indicates that magnetisation is in the same direction as the magnetising field.

  3. 3

    Add for 3 marks

    When a material is placed in a magnetic field, its atomic or molecular magnetic dipoles respond to the field.

Practice

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