05Class 12 Physics

Magnetism and Matter formulas

Bar magnet and magnetic material formulas for Magnetism and Matter. It's a short sheet, and these results mirror the electric dipole.

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Bar magnet

Field on the axis: $\displaystyle B = \frac{\mu_0}{4\pi}\frac{2m}{r^3}$
Field on the equator: $\displaystyle B = \frac{\mu_0}{4\pi}\frac{m}{r^3}$
Torque in a uniform field: $\displaystyle \vec\tau = \vec m\times\vec B$
Potential energy: $\displaystyle U = -\vec m\cdot\vec B$
Time period in a field: $\displaystyle T = 2\pi\sqrt{\frac{I}{mB}}$
Gauss's law for magnetism: $\displaystyle \oint\vec B\cdot d\vec A = 0$
There are no isolated magnetic poles.

Magnetisation: $\displaystyle M = \frac{m_{\text{net}}}{V}$
Total field: $\displaystyle B = \mu_0(H + M)$
Susceptibility: $\displaystyle \chi = \frac{M}{H}$
Permeability: $\displaystyle \mu = \mu_0\mu_r, \quad \mu_r = 1 + \chi$
Curie's law: $\displaystyle \chi = \frac{C\mu_0}{T}$
For paramagnetic materials.

Thinking magnetic field lines start and end at poles. They form closed loops, passing through the magnet.
Mixing up the types: diamagnetic has small negative χ, paramagnetic small positive χ, and ferromagnetic large positive χ.
Expecting diamagnetism to change with temperature the way paramagnetism does. Curie's law is for paramagnets.

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