Physics · Ch 5 — Magnetism and Matter

Points to Ponder

The practical use of magnets for direction-finding existed for about two thousand years before physicists, around 1800 AD, finally explained magnetism using moving charges and currents. This shows that a deep scientific theory is not always required to build useful technology; however, the best progress happens when science and engineering develop together, each helping the other.
Isolated magnetic north or south poles (magnetic monopoles) do not exist. Cutting a magnet always produces two complete magnets, each with both poles. In contrast, isolated electric charges (like the electron) do exist, and electric charge is quantised: every charge is an integer multiple of $|e| = 1.6 \times 10^{-19}\ \text{C}$ . Why monopoles are absent and why charge is quantised are still open questions.
Because magnetic monopoles are absent, magnetic field lines never start or end — they always form continuous closed loops. Electric field lines, however, begin on positive charges and end on negative charges (or go to infinity).
A tiny difference in magnetic susceptibility $\chi$ leads to completely opposite magnetic behaviour. For diamagnetic materials, $\chi \approx -10^{-5}$ , while for paramagnetic materials, $\chi \approx +10^{-5}$ . The table below summarises the key magnetic quantities:

Physical quantity	Symbol	Nature	Dimensions	SI Unit	Remarks
Permeability of free space	$\mu_0$	Scalar	$[\text{MLT}^{-2}\text{A}^{-2}]$	$\text{T m A}^{-1}$	$\mu_0/4\pi = 10^{-7}$
Magnetic field / Magnetic induction / Magnetic flux density	$\mathbf{B}$	Vector	$[\text{MT}^{-2}\text{A}^{-1}]$	T (tesla)	$1\ \text{T} = 10^4\ \text{G}$
Magnetic moment	$\mathbf{m}$	Vector	$[\text{L}^{-2}\text{A}]$	$\text{A m}^2$	—
Magnetic flux	$\phi_B$	Scalar	$[\text{ML}^2\text{T}^{-2}\text{A}^{-1}]$	W (weber)	$\text{W} = \text{T m}^2$
Magnetisation	$\mathbf{M}$	Vector	$[\text{L}^{-1}\text{A}]$	$\text{A m}^{-1}$	Magnetic moment per volume
Magnetic intensity	$\mathbf{H}$	Vector	$[\text{L}^{-1}\text{A}]$	$\text{A m}^{-1}$	$\mathbf{B} = \mu_0(\mathbf{H} + \mathbf{M})$
Magnetic susceptibility	$\chi$	Scalar	—	—	$\mathbf{M} = \chi \mathbf{H}$
Relative magnetic permeability	$\mu_r$	Scalar	—	—	$\mathbf{B} = \mu_0 \mu_r \mathbf{H}$
Magnetic permeability	$\mu$	Scalar	$[\text{MLT}^{-2}\text{A}^{-2}]$	$\text{T m A}^{-1}$	$\mu = \mu_0 \mu_r$ , $\mathbf{B} = \mu \mathbf{H}$