MAGNETISM AND MATTER

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17 Terms

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Bar Magnet

  • It has 2 equal and opposite poles

  • When freely suspended, it orients itself along the geographic north and south

  • When a bar magnet is cut into 2 pieces, it forms 2 magnets with the north and south pole

  • There is no magnetic monopole (isolated poles cannot exist)

  • When a bar magnet is cut laterally, its pole strength decreases and when it is cut transversely its pole strength remains the same

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Magnetic Moment

m = NIA

m = p x l (p-pole strength,l=length)

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Magnetic Field Lines

Imaginary lines that represent the magnetic field around a magnet

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Properties of Magnetic Field Lines

  • They form continuous curves that originate from the north pole and ends at south pole outside and it goes from south pole to north pole inside

  • They never intersect

  • They are closer together in areas of stronger magnetic field and spread out in areas of weaker magnetic field

  • The density of magnetic field lines is proportional to the strength of the magnetic field (greater the number of field lines per unit area, stronger the magnetic field)

  • If the magnetic field lines are parallel, then the magnetic field is uniform

  • The direction of the magnetic field is given by the tangent to the field lines at that point

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Magnetic field due to a Bar Magnet as a Solenoid

At an axial point,

B = (µ/4π)(2m/r³)

At an equatorial point,

B = (-µₒ/4π)(m/r³)

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Dipole in a uniform magnetic field

𝜏 = mxB = mbsinθ

U = -m.B = mbcosθ

Special Cases:

  1. If  θ = 0º:

    • 𝜏 = 0

    • U = -mB

    • Stable

  2. If  θ = 90º:

    • 𝜏 = mb

    • U = 0

  3. If  θ = 180º:

    • 𝜏 = 0

    • U = mb

    • Unstable

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Dipole Analogy of Electrostatics vs Magnetism

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Gauss Law for Magnetism

The closed integral of the magnetic field over a surface is zero

∲B.dA = 0

This indicates the non-existence of magnetic monopoles

The net magnetic flux through any closed surface is zero

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Magnetisation (M)

Net magnetic moment acquired by a sample per unit volume when it is placed in a magnetic field

M = mnet/V

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Magnetic Field Intensity (H)

It is defined as the ratio of magnetic field induction to the permeability of the medium

H = B/µ

In a solenoid,

H=nI

Unit - A/m

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Relation between B, H and M

Bₘ = µₒM

B = µₒ(H+M)

B = µH

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Magnetic Susceptibility (χ)

It is the ratio of magnetisation to the magnetic field intensity

χ = M/H

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Magnetic Permeability

The ability of a material to become magnetised

µᵣ = 1+χ

µ = µᵣµₒ

µᵣ (relative permeability - the ratio of permeability of medium to the permeability of free space)

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Classification of Materials

  1. Diamagnetic

  2. Paramagnetic

  3. Ferromagnetic

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Diamagnetic Materials

  • These materials exhibit negative magnetization, i.e., the molecules align opposite the aligned magnetic field.

  • Diamagnetic materials have filled orbitals.

  • They have negative susceptibility: χ < 0

    • Since χ < 0, M is opposite to H.

  • The relative permeability of diamagnetic substances μr < 1.

    • μ < μ₀.

  • When a diamagnetic material can move in an external magnetic field, it goes from stronger to weaker regions.

  • When a diamagnetic material is placed in an external magnetic field and cannot move, the field lines expel out of it.

  • A diamagnetic material will be weakly repelled in the presence of an external field.

  • Superconducting materials (materials that offer 0 resistance) have their susceptibility as -1, then B will be 0. Hence superconductors are diamagnetic and repel all magnetic field lines out of it.

  • Examples: Bismouth, Cu, Pb, N₂, Si, H₂O, NaCl.

<ul><li><p>These materials exhibit negative magnetization, i.e., the molecules align opposite the aligned magnetic field.</p></li><li><p>Diamagnetic materials have filled orbitals.</p></li><li><p>They have negative susceptibility: χ &lt; 0</p><ul><li><p>Since χ &lt; 0, M is opposite to H.</p></li></ul></li><li><p>The relative permeability of diamagnetic substances μr &lt; 1.</p><ul><li><p>μ &lt; μ₀.</p></li></ul></li><li><p>When a diamagnetic material can move in an external magnetic field, it goes from stronger to weaker regions.</p></li><li><p>When a diamagnetic material is placed in an external magnetic field and cannot move, the field lines expel out of it.</p></li><li><p>A diamagnetic material will be weakly repelled in the presence of an external field.</p></li><li><p>Superconducting materials (materials that offer 0 resistance) have their susceptibility as -1, then B will be 0. Hence superconductors are diamagnetic and repel all magnetic field lines out of it.</p></li><li><p>Examples: Bismouth, Cu, Pb, N₂, Si, H₂O, NaCl.</p></li></ul>
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Paramagnetic Materials

  • In the presence of an external field, the molecules orient themselves along the direction of the field.

  • They tend to move from weaker to stronger regions of the magnetic field.

  • They are very weakly attracted when placed in a magnetic field.

  • The magnetic field lines will pass through (converge/concentrate) a paramagnetic material.

  • The susceptibility of the paramagnet is greater than zero: χ > 0
    μr > 1
    μ > μ₀

  • As temperature increases, the molecules have thermal agitation, so their net magnetic moment decreases. Hence, the susceptibility of a paramagnet depends on temperature.
    χ ∝ 1/T (For paramagnets)

  • Examples: Al, Na, Ca, O₂, CuCl₂

<ul><li><p>In the presence of an external field, the molecules orient themselves along the direction of the field.</p></li><li><p>They tend to move from weaker to stronger regions of the magnetic field.</p></li><li><p>They are very weakly attracted when placed in a magnetic field.</p></li><li><p>The magnetic field lines will pass through (converge/concentrate) a paramagnetic material.</p></li><li><p>The susceptibility of the paramagnet is greater than zero: χ &gt; 0<br>μr &gt; 1<br>μ &gt; μ₀</p></li><li><p>As temperature increases, the molecules have thermal agitation, so their net magnetic moment decreases. Hence, the susceptibility of a paramagnet depends on temperature.<br>χ ∝ 1/T (For paramagnets)</p></li><li><p>Examples: Al, Na, Ca, O₂, CuCl₂</p><p></p></li></ul>
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Ferromagnetic Materials

  • Ferromagnetic materials are paramagnets and they form domains.

  • Domains are groups of atoms/molecules that behave as a single unit.

  • The susceptibility of ferromagnetic materials is very high:
    χ ≫ 0
    μr ≫ 1
    μ ≫ μ₀

  • As temperature increases, the domains will break, and the ferromagnet becomes a paramagnet.

  • Ferromagnets are classified as:

    • Hard Ferromagnet: Retain magnetic property even after removing from the external field.

    • Soft Ferromagnet: Does not retain the magnetic property.

  • Examples:

    • Hard Ferromagnet: Alnico (Alloy), Loadstone

    • Soft Ferromagnet: Fe, Ni, Co, Gadolinium

<ul><li><p>Ferromagnetic materials are paramagnets and they form domains.</p></li><li><p>Domains are groups of atoms/molecules that behave as a single unit.</p></li><li><p>The susceptibility of ferromagnetic materials is very high:<br>χ ≫ 0<br>μr ≫ 1<br>μ ≫ μ₀</p></li><li><p>As temperature increases, the domains will break, and the ferromagnet becomes a paramagnet.</p></li><li><p>Ferromagnets are classified as:</p><ul><li><p>Hard Ferromagnet: Retain magnetic property even after removing from the external field.</p></li><li><p>Soft Ferromagnet: Does not retain the magnetic property.</p></li></ul></li><li><p>Examples:</p><ul><li><p>Hard Ferromagnet: Alnico (Alloy), Loadstone</p></li><li><p>Soft Ferromagnet: Fe, Ni, Co, Gadolinium<br></p></li></ul></li></ul>