# Magnetic moment of current loop

From what I have learnt, the magnetic moment of a current carrying loop is $$\pmb{\mu} = NI \mathbf{A}.$$

But what is written in this book Modern atomic and nuclear physics by Fuzia Yang, I am not able to understand.

4.1.1 Classical Expression

It is well known in classical electromagnetism that the mangetic moment $$\mu$$ associated with a small electric current may be expressed as (see Fig. 4.1(a)) $$\pmb{\mu} = \frac{i}{c} S \mathbf{n}_0$$ where $$i$$ is the electric current in the sense of positive charge flow, $$c$$ is the speed of light ($$c=1$$ in this equation in "reduced" units based on the SI system of units), $$S$$ is the area enclosed by the current circuit, and $$\mathbf{n}_0$$ is a unit vector normal to the plane of the circuit.

It would be great help if somebody could provide a clue for how the two are connected.

• Hello! It is preferable to type out screenshots or images of text; for formulae, one can use MathJax. Thanks! Apr 20, 2022 at 17:20

From what I have learnt, the magnetic moment of a current carrying loop is $$\pmb{\mu} = NI \mathbf{A}.$$
It is well known in classical electromagnetism that the mangetic moment $$\mu$$ associated with a small electric current may be expressed as (see Fig. 4.1(a)) $$\pmb{\mu} = \frac{i}{c} S \mathbf{n}_0$$ where $$i$$ is the electric current in the sense of positive charge flow, $$c$$ is the speed of light ($$c=1$$ in this equation in "reduced" units based on the SI system of units), $$S$$ is the area enclosed by the current circuit, and $$\mathbf{n}_0$$ is a unit vector normal to the plane of the circuit.
He is just using different symbols and considering only one loop winding (not $$N$$ windings). He is also using different units and, as he writes, you can set $$c$$ to 1 to convert to "reduced" SI units.
The translation of symbols from the bottom equation to the top equation is: $$S\mathbf n_0 \to \mathbf A$$ $$i \to I$$ $$c \to 1$$