#superconductors

Diamagnetism, Paramagnetism and Ferromagnetism

A material with \( \mu_r = 0 \) completely expels magnetic fields and is classified as:

**Diamagnetism** exhibits small negative susceptibility χ ≈ -10⁻⁵ to -10⁻⁶, weakly repelled from stronger to weaker field regions, no permanent moment, induced moment opposite to B, present in all materials but dominated by other effects. Superconductor perfect diamagnet with χ = -1, complete field expulsion. A material with μ_r = 0 (and chi = -1 ) exhibits perfect diamagnetism, characteristic of a superconductor due to the Meissner effect. Substituting values gives Superconductor, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

Ref: NCERT > Physics Book > Magnetism and Matter > Diamagnetism, Paramagnetism and Ferromagnetism

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Torque on Magnetic Dipole and Potential Energy

Which material exhibits perfect diamagnetism with \( \chi = -1 \) and is used in levitating trains?

**Magnetic dipole in uniform field** experiences torque τ = m B sinθ and potential energy U = -m·B = -m B cosθ, minimum -mB when aligned (θ=0°), maximum +mB at anti-alignment (θ=180°). Work done rotating from θ₁ to θ₂ equals ΔU = mB(cosθ₁ - cosθ₂). Superconductors exhibit perfect diamagnetism with chi = -1 due to the Meissner effect and are used in applications like magnetically levitated trains. Substituting values gives Superconductor, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

Ref: NCERT > Physics Book > Magnetism and Matter > Torque on Magnetic Dipole and Potential Energy

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Magnetic Field Lines, Bar Magnet and Dipole Moment

The reason a superconductor can levitate a magnet is:

**Magnetic field lines** form continuous closed loops, direction given by tangent at point, density indicates field strength. Unlike electric field lines, magnetic lines never intersect because unique field direction exists at each point, and bar magnet possesses dipole moment m = N I A directed from south to north pole inside magnet. Superconductors exhibit perfect diamagnetism (Meissner effect), expelling all magnetic field lines from their interior by inducing surface currents that create an opposing field. This repulsion allows them to levitate a magnet, a phenomenon unique to their zero permeability state. Substituting values gives Complete expulsion of magnetic fields, which matches expected magnitude for this

Ref: NCERT > Physics Book > Magnetism and Matter > Magnetic Field Lines, Bar Magnet and Dipole Moment

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Torque on Magnetic Dipole and Potential Energy

A material that conducts electricity perfectly and repels magnetic fields is likely operating as:

**Torque on magnetic dipole** in uniform field B is τ = m × B, magnitude τ = m B sinθ, m moment (A·m²), B field (T), θ angle between m and B (degrees). Torque tends to align moment with field, zero at θ = 0°, maximum mB at 90°, direction given by right-hand rule. Superconductors, when below their critical temperature, exhibit zero electrical resistance (perfect conductivity) and perfect diamagnetism (repelling magnetic fields via the Meissner effect), a unique combination not seen in other materials. Substituting values gives A superconductor, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque

Ref: NCERT > Physics Book > Magnetism and Matter > Torque on Magnetic Dipole and Potential Energy

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