Class 12 Physics Magnetism and Matter Formulas

Magnetic Dipole Moment due to a Bar magnet

Magnetic Field due to a Bar Magnet at a distance r from the center 

• On the axial line

$$B_{\text{axial}}=\frac{{\mu }_0}{4\pi }\cdot \frac{2M}{r^3}$$

• On the equatorial line:

$$B_{\text{equatorial}} = \frac{\mu_0}{4\pi} \cdot \frac{M}{r^3}$$

Torque on a Bar Magnet due to a Uniform Magnetic Field

$$\boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}$$

Work Done in Rotating the Bar Magnet in a Uniform Magnetic Field

• In rotating θ :

$$U = - \mathbf{m} \cdot \mathbf{B} = - m B \cos \theta$$

• In rotating the dipole from angle $\theta_1$to $\theta_2$:

Magnetisation (M)

It is a measure of a material to be magnetised when it is placed in a magnetic field. 

$$M<br>=\frac{\sum m_{\mathrm{net}}}{V}$$

Magnetic Intensity (H)

It is a measure of a magnet or current to produce a magnetic field.

$$\mathbf{H}=\frac{\mathbf{B}}{{\mu }_0}-\mathbf{M}$$

Magnetic Susceptibility

It is a measure of how much a material can be magnetised in an external magnetic field.

$$\begin{array}{cccc}& \mathbf{M}=\chi \mathbf{H}& & \text{<br>}\end{array}$$

Magnetic Flux Density

It is another way of measuring the magnetic field.

$$\begin{array}{cc}& \mathbf{B}={\mu }_0(1+\chi )\mathbf{H}\end{array}$$

$$\begin{array}{ccc}B\; ={\mu }_0{\mu }_r\mathbf{H}=\mu \mathbf{H}& & \text{<br>}\end{array}$$

Relation Between B, H, and M

$$\mathbf{B}={\mu }_0(\mathbf{H}+\mathbf{M})$$

Relation Between μ₀ and χ

$\mu = \mu_0 \mu_r$

$${\mu }_r=1+\chi$$

$$\mu ={\mu }_0(1+\chi )$$