Which of the following statements is correct for diamagnetic materials? (A) $\mu_r

Question

Which of the following statements is correct for diamagnetic materials? (A) $\mu_r<1$ (B) $\chi$ is negative and low (C) $\chi$ does not depend on temperature (D) All of the above

Accepted Answer

Concept understanding — Diamagnetism

Diamagnetism: The Quiet Repulsion

Imagine you bring a magnet near a piece of copper or water. Nothing dramatic happens — no strong pull like iron, no noticeable push. But if you had a very sensitive scale, you'd detect a tiny repulsion. The material is pushed away, ever so slightly. That's diamagnetism.

Why does this happen? The key is that in a diamagnetic material, every atom has zero net magnetic moment to begin with. All its electrons are paired up — each electron's tiny magnetic field is cancelled by its partner. The atom is magnetically neutral.

Now bring an external magnetic field. Something subtle occurs: the field slightly distorts the motion of the orbiting electrons. According to Lenz's law, the electrons respond by creating a tiny induced magnetic moment that opposes the applied field. This is like a weak electromagnetic shield — the material generates its own field pointing opposite to the external one.

Note

This induced moment is temporary. Remove the external field, and the material returns to being magnetically neutral. No permanent magnetism remains.

The result? The material is weakly repelled. The strength of this repulsion is measured by magnetic susceptibility $\chi$ , which for diamagnets is small and negative — typically around $-10^{-5}$ to $-10^{-6}$ .

The Precise Statement

Diamagnetism is the property of materials whose atoms have no permanent magnetic dipole moment. When placed in an external magnetic field $\mathbf{B}$ , the orbital motion of electrons induces a magnetic moment $\mathbf{m}$ opposite to $\mathbf{B}$ , leading to a negative magnetic susceptibility $\chi < 0$ .

\mathbf{m} = -\frac{e^2}{6m_e} \langle r^2 \rangle \mathbf{B}

The susceptibility is:

Small in magnitude ( $|\chi| \sim 10^{-5}$ )
Negative (repulsion)
Independent of temperature — because it arises from orbital motion, not from thermal alignment of permanent moments

Important

Unlike paramagnets and ferromagnets, diamagnetism is present in all materials. But it's usually masked by stronger magnetic effects. Only in materials with no unpaired electrons (like copper, bismuth, water, and most organic compounds) does diamagnetism become the dominant response.

Common Examples

Material	$\chi$ (approx.)	Behaviour
Bismuth	$-1.66 \times 10^{-4}$	Strongest diamagnet among elements
Copper	$-9.7 \times 10^{-6}$	Weakly repelled
Water	$-9.0 \times 10^{-6}$	Pure water is diamagnetic
Graphite	$-1.6 \times 10^{-4}$	Anisotropic — stronger along certain axes

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Check each statement against section 11.5.1. (A) Since $\mu_r=1+\chi$ and $\chi$ is negative for diamagnetic materials (Table 11.2 gives a range of about $-10^{-3}$ to $-10^{-5}$ ), $\mu_r$ is slightly less than 1 -- true. (B) By definition, diamagnetism is characterised by a small, negative susceptibility -- true, and directly confirmed by the negative $\chi$ values for silicon, bismuth, copper, etc. in Table 11.1. (C) Diamagnetism arises from field-INDUCED currents opposing the applied field (Lenz's law acting on paired electron orbits), not from the thermal (re-)orientation of pre-existing atomic moments the way paramagnetism and ferromagnetism do -- so, …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

Showing the 12 most recent of 16 on this concept.

CBSE 2026Set ANNUAL1 markMCQ
$Q. Super conductor material exhibit perfectly$
(a) ferromagnetism
(b) paramagnetism
(c) diamagnetism
(d) strong ferromagnetism
›Reveal solutionSolution

Superconductors show the Meissner effect - they expel magnetic field lines completely from their interior, which is the signature of perfect diamagnetism.

Below their critical temperature, superconductors develop surface currents that exactly cancel any external magnetic field inside the material, so B_inside = 0. A material with a magnetic susceptibility …

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CBSE 2025Set 55/6/11 markMCQ
$Q. A piece of a diamagnetic material, free to move when placed in a uniform magnetic field: (A) moves along the field (B) moves opposite to the field (C) moves perpendicular to the field (D) does not move at all$
›Reveal solutionSolution
A diamagnetic material experiences no net force in a uniform magnetic field because the induced magnetic moment opposes the field but the field gradient is zero — so the material does not move. The correct option is (D).

Why This Works

The key is the word uniform. A uniform magnetic field has the same strength and direction at every point. For any material to experience a net force, the field must be non-uniform — there must be a gradient. Diamagnetism is a weak, induced effect: when placed in a field, the material develops a tiny magnetic moment opposite to the field. But in a uniform field, equal and opposite forces on the north and south poles of this induced dipole cancel out exactly. No net force means no motion.

Watch out

A classic mistake is to think diamagnetic materials are "repelled" by magnets — that's true only in a non-uniform field (like near a pole). In a uniform field, repulsion doesn't produce motion because the force is zero everywhere.

Step-by-Step Reasoning

Understand the nature of diamagnetism

Diamagnetic materials have no permanent magnetic dipoles. When placed in an external magnetic field $\vec{B}$ , the orbital motion of electrons changes slightly, inducing a magnetic moment $\vec{m}$ that is opposite to $\vec{B}$ . This is a weak effect, present in all materials but usually swamped by paramagnetism or ferromagnetism.

Force on a magnetic dipole in a field

The force on a magnetic dipole $\vec{m}$ in a magnetic field $\vec{B}$ is given by:

$\vec{F} = \nabla (\vec{m} \cdot \vec{B})$
For a diamagnetic material, $\vec{m}$ is antiparallel to $\vec{B}$ , so $\vec{m} \cdot \vec{B} = -|\vec{m}||\vec{B}|$ . The force becomes:
$\vec{F} = -\nabla (|\vec{m}||\vec{B}|)$
This force depends on the gradient of the field magnitude.

Apply to a uniform field In a uniform magnetic field, $\vec{B}$ is constant in magnitude and direction everywhere. Therefore:

$\nabla |\vec{B}| = 0$
Consequently, $\vec{F} = 0$ at all points. The material experiences no net force.

What about torque? …
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CBSE 2025Set X11 mark
$Q. Water is an example for ________ material.$
›Reveal solutionSolution

diamagnetic Water has no permanent atomic magnetic moment and is weakly repelled by a magnetic field (relative permeability slightly less than 1), so it is a diamagnetic material. …

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CBSE 2024Set A11 markMCQ
$Q. The universal property among all substances is$
(a) Diamagnetism
(b) Paramagnetism
(c) Ferromagnetism
(d) Non-magnetism
›Reveal solutionSolution

(a) Diamagnetism …

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CBSE 2024Set IMPROVEMENT1 mark
$\chi$
›Reveal solutionSolution

Small, negative susceptibility is the defining signature of a diamagnetic material.

Magnetic susceptibility $\chi$ measures how strongly a material responds to an applied magnetic field. Diamagnetic materials have a small, negative $\chi$ (typically of order $-10^{-5}$ ), meaning they are weakly magnetised opposite to the applied field. (In contrast, paramagnetic materials have small positive $\chi$ , …

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CBSE 2024Set A1 mark
$Q. Fill in the blank with appropriate word: The substances which have negative magnetic tendency are called ______ substances.$
›Reveal solutionSolution
A negative magnetic susceptibility (χ < 0) identifies a diamagnetic substance.

Magnetic materials are classified by their magnetic susceptibility χ, defined by $M = \chi H$ (M = magnetisation, H = magnetising field).

Diamagnetic substances have a small negative susceptibility — they get weakly magnetised opposite to the applied field and are repelled by it (e.g., bismuth, copper, water). …
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CBSE 2023Set 55/1/11 markMCQ
$Q. A diamagnetic substance is brought near the north or south pole of a bar magnet. It will be :$
(a) repelled by both the poles.
(b) attracted by both the poles.
(c) repelled by the north pole and attracted by the south pole.
(d) attracted by the north pole and repelled by the south pole.
›Reveal solutionSolution
Diamagnetic materials develop an induced magnetic moment opposite to the applied field, causing repulsion regardless of which pole approaches them. The answer is (a).

Why diamagnetic materials behave this way

When you place any material in a magnetic field, the field tries to align the tiny atomic current loops inside it. Most materials respond in one of three ways: ferromagnetic (strong attraction), paramagnetic (weak attraction), or diamagnetic (weak repulsion).

Diamagnetic substances have no permanent magnetic moments. Their atoms have paired electrons whose magnetic effects cancel out. But here's the key: when an external magnetic field approaches, it induces tiny currents in the electron orbits through Lenz's law. These induced currents create a magnetic moment that opposes the applied field—nature's way of resisting change.

Think of it this way: if you bring the north pole of a bar magnet close to a diamagnetic material, the material develops a north pole on the side facing the magnet. Two north poles repel. If you bring the south pole close instead, the material develops a south pole facing it. Two south poles also repel.

Step-by-step reasoning

The external field induces a moment

When either pole of the bar magnet approaches, the diamagnetic substance experiences a non-uniform magnetic field. This field penetrates the material and alters the electron orbital motion.

Lenz's law governs the response

The induced magnetic moment $\vec{m}_{\text{induced}}$ is always antiparallel to the applied field $\vec{B}_{\text{ext}}$ :

$\vec{m}_{\text{induced}} = -\chi \vec{B}_{\text{ext}}$
where $\chi > 0$ is the (positive) diamagnetic susceptibility. The negative sign is the signature of diamagnetism.

The force is always repulsive A magnetic dipole in a non-uniform field experiences a force:

$\vec{F} = \nabla(\vec{m} \cdot \vec{B})$
Since $\vec{m}_{\text{induced}}$ points opposite to $\vec{B}$ , the dot product $\vec{m} \cdot \vec{B}$ is negative and decreases as the field strengthens. The gradient points the dipole toward weaker field regions—away from the magnet pole.

Pole identity doesn't matter …
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CBSE 2023Set 55/4/11 markMCQ
$Q. The magnetic field lines near a substance are as shown in the figure. The substance is : (A) Copper (B) Iron (C) Sodium (D) Aluminium$
›Reveal solutionSolution

The field lines bow away from the substance, indicating the material expels the field — the hallmark of a diamagnetic substance. Of the options, only copper is diamagnetic.

Understanding magnetic response: how materials interact with external fields

When you place a material in an external magnetic field, its atoms respond in one of three fundamental ways, depending on their electronic structure:

Diamagnetic materials (like copper, gold, bismuth) have all electrons paired. The external field induces tiny circulating currents in the electron clouds that oppose the applied field (Lenz's law at the atomic scale). The net effect: the material develops a very weak magnetization opposite to the external field, so the field inside the material is slightly weaker than outside. Relative permeability $\mu_r < 1$ (typically $0.99999…$ ). Field lines are repelled or expelled from the substance.

Paramagnetic materials (like aluminium, sodium, platinum) have unpaired electrons with permanent magnetic moments. These moments normally point randomly, but the external field aligns them along the field direction. The material develops a weak magnetization in the same direction as the applied field, so the field inside is slightly stronger. Relative permeability $\mu_r > 1$ (just barely, say $1.00002$ ). Field lines are drawn into the substance.

Ferromagnetic materials (iron, cobalt, nickel) also have unpaired electrons, but with strong exchange coupling between neighbouring atoms. They form magnetic domains and can be permanently magnetized. In an external field, domains align strongly, and the field inside becomes much stronger. Relative permeability $\mu_r \gg 1$ (thousands). Field lines crowd into the substance dramatically.

Reading the figure

Figure — CBSE 2023 55/4/1 Q3

The diagram shows field lines approaching a rectangular bar from the left. Crucially, the lines bow outward around the bar — they avoid entering it. The density of lines inside the bar is lower than in the surrounding space. This is the signature pattern of field expulsion.

Watch out

A common mistake is to confuse "lines bending" with "attraction." If lines crowd into a material (higher density inside), the material is para- or ferromagnetic. If lines spread out and avoid the material (lower density inside), it is diamagnetic.

Classifying the options

Let's identify the magnetic character of each substance: …
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CBSE 2023Set ANNUAL1 markMCQ
$Q. An example of Diamagnetic material is ________.$
(a) Nickel
(b) Water
(c) Aluminium
(d) Iron
›Reveal solutionSolution

Water is diamagnetic; nickel and iron are ferromagnetic and aluminium is paramagnetic, so water is the correct choice.

Working

Diamagnetic materials have no permanent atomic magnetic dipole moment. When placed in an external magnetic field, they develop a weak induced moment opposite to the applied field and are weakly repelled by it (small negative suscep …

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CBSE 2022Set ANNUAL1 markMCQ
$\chi$
(a) $\chi$ is negative
(b) $\chi$ is positive and small
(c) $\chi$ is large and positive
(d) $\chi$ is zero
›Reveal solutionSolution
Susceptibility $\chi=M/H$ measures how strongly a material magnetises in response to a field $H$ . Diamagnetic substances develop a magnetisation opposite to $H$ , so $\chi<0$ .

Definition of susceptibility

For a magnetic material placed in an external field of intensity $H$ , the magnetisation $M$ produced in it is

$M = \chi H$

where $\chi$ is the magnetic susceptibility, a dimensionless number characterising the material's magnetic response.

Classifying materials by $\chi$

Diamagnetic: $\chi$ is small and negative (typically $-10^{-5}$ to $-10^{-6}$ ). The induced dipole moments oppose $\vec H$ , so the material is feebly repelled by a magnet (e.g. bismuth, copper, water).

Paramagnetic: $\chi$ is small and positive (typically $10^{-3}$ to $10^{-5}$ ). The material is feebly attracted (e.g. aluminium, sodium). …
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CBSE 2020Set ANNUAL1 mark
$Q. What is diamagnetic substances?$
›Reveal solutionSolution
Diamagnetic substances develop a weak magnetisation opposite to an applied magnetic field and are repelled, however weakly, by magnets.

When certain substances are placed in an external magnetic field $B$ , the field induces a small magnetic moment in the material directed opposite to $B$ . Such substances are called diamagnetic substances.

Key properties:

Magnetic susceptibility $\chi$ is small and negative.

Relative permeability $\mu_r$ is slightly less than 1.

They are weakly repelled by a strong magnet (move from stronger to weaker field regions).

Magnetisation is independent of temperature (mostly) and disappears when the external field is removed. …
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CBSE 2019Set ANNUAL1 mark
$Q. What is the value of relative magnetic permeability of perfectly diamagnetic substance?$
›Reveal solutionSolution

A perfectly diamagnetic material completely expels magnetic field lines from its interior, so its relative permeability is zero.

…

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Q.Which of the following statements is correct for diamagnetic materials? (A) μr<1\mu_r<1μr​<1 (B) χ\chiχ is negative and low (C) χ\chiχ does not depend on temperature (D) All of the above

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Q.Which of the following statements is correct for diamagnetic materials? (A) $\mu_r<1$ (B) $\chi$ is negative and low (C) $\chi$ does not depend on temperature (D) All of the above

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