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CLASS 12 • PHYSICS
Magnetism & Matter
1. The Bar Magnet
Magnetic Dipole Moment
$\vec{M} = m(2\vec{l})$
Direction: South to North
Field on Axial Line
$B_{ax} = \frac{\mu_0}{4\pi} \frac{2M}{r^3}$
Field on Equatorial Line
$B_{eq} = \frac{\mu_0}{4\pi} \frac{M}{r^3}$
2. Torque & Gauss Law
Torque in B Field
$\vec{\tau} = \vec{M} \times \vec{B} = MB \sin\theta$
Potential Energy
$U = -\vec{M} \cdot \vec{B} = -MB \cos\theta$
Gauss Law for Magnetism
$\oint \vec{B} \cdot d\vec{A} = 0$
Monopoles do not exist
3. Earth's Magnetism
Horizontal Component
$B_H = B \cos\delta$
Vertical Component
$B_V = B \sin\delta$
$\delta$ = Angle of Dip
Resultant Relation
$B = \sqrt{B_H^2 + B_V^2}$
Angle of Dip
$\tan\delta = \frac{B_V}{B_H}$
4. Magnetic Terms
Magnetization (I)
$I = \frac{M_{net}}{Volume}$
Unit: A/m
Magnetic Intensity (H)
$H = \frac{B_0}{\mu_0} = nI$
Unit: A/m (External Field)
Susceptibility ($\chi$)
$\chi = \frac{I}{H}$
5. Important Relations
Total Magnetic Field
$B = \mu_0 (H + I)$
Relative Permeability
$\mu_r = 1 + \chi$
Absolute Permeability
$\mu = \mu_0 \mu_r$
6. Curie's Law
For Paramagnetic Materials
$\chi = \frac{C}{T}$
Susceptibility decreases with Temp
For Ferromagnetic
$\chi = \frac{C}{T - T_c}$
$T_c$ = Curie Temperature
7. Common Exam Traps
- ⚠️ Angle of Dip: It is $90^\circ$ at Poles (Vertical field) and $0^\circ$ at Equator (Horizontal field).
- ⚠️ Units of H & I: Both have the SAME unit (Amperes/meter). Don't confuse with B (Tesla).
- ⚠️ Work Done: To rotate magnet from $\theta_1$ to $\theta_2$, work is $MB(\cos\theta_1 - \cos\theta_2)$. If stable to unstable ($\theta=0 \to 180$), Work = $2MB$.
8. Golden Theory Rules
- Diamagnetic: $\chi$ is small and negative ($-1 \le \chi < 0$). Repelled by magnets.
- Paramagnetic: $\chi$ is small and positive. Weakly attracted.
- Ferromagnetic: $\chi$ is very large and positive. Strongly attracted.
- Soft Iron: Low Retentivity, Low Coercivity (Best for Electromagnets).
- Steel: High Retentivity, High Coercivity (Best for Permanent Magnets).
