Physics · Ch 5 — Magnetism and Matter

Summary

Magnetic dipole moment of a bar magnet: $\vec{m} = m \cdot 2\vec{l}$ , where $m$ is pole strength and $2\vec{l}$ is the separation between poles.
Magnetic field due to a bar magnet at an axial point: $B_{\text{axial}} = \frac{\mu_0}{4\pi} \frac{2m}{r^3}$ ; at an equatorial point: $B_{\text{equatorial}} = \frac{\mu_0}{4\pi} \frac{m}{r^3}$ .
Torque on a magnetic dipole in a uniform field: $\vec{\tau} = \vec{m} \times \vec{B}$ , magnitude $\tau = mB \sin\theta$ .
Potential energy of a magnetic dipole: $U = -\vec{m} \cdot \vec{B} = -mB \cos\theta$ .
Gauss’s law for magnetism: $\oint \vec{B} \cdot d\vec{A} = 0$ — magnetic monopoles do not exist; field lines form closed loops.
Earth’s magnetism: Three elements — declination (angle between geographic and magnetic meridian), dip (angle of field with horizontal), horizontal component $B_H = B_E \cos \delta$ (where $\delta$ is dip angle).
Magnetic materials:
- Diamagnetic — weak repulsion, $\chi_m < 0$ , small negative susceptibility (e.g., bismuth).
- Paramagnetic — weak attraction, $\chi_m > 0$ , small positive (e.g., aluminium).
- Ferromagnetic — strong attraction, large positive $\chi_m$ , exhibits hysteresis and Curie temperature (e.g., iron). …