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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

CBSECBSE Class XII Board 2025MCQ· 1mImportance★★★★★
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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

  1. Understand the nature of diamagnetism

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

  2. Force on a magnetic dipole in a field

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

F⃗=∇(m⃗⋅B⃗)\vec{F} = \nabla (\vec{m} \cdot \vec{B})

For a diamagnetic material, m⃗\vec{m} is antiparallel to B⃗\vec{B}, so m⃗⋅B⃗=−∣m⃗∣∣B⃗∣\vec{m} \cdot \vec{B} = -|\vec{m}||\vec{B}|. The force becomes:

F⃗=−∇(∣m⃗∣∣B⃗∣)\vec{F} = -\nabla (|\vec{m}||\vec{B}|)

This force depends on the gradient of the field magnitude.

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

∇∣B⃗∣=0\nabla |\vec{B}| = 0

Consequently, F⃗=0\vec{F} = 0 at all points. The material experiences no net force.

  1. What about torque? …

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