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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.

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    $\begingroup$ Hello! It is preferable to type out screenshots or images of text; for formulae, one can use MathJax. Thanks! $\endgroup$
    – jng224
    Apr 20, 2022 at 17:20

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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.

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: $$ S\mathbf n_0 \to \mathbf A $$ $$ i \to I $$ $$ c \to 1 $$

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  • $\begingroup$ Ok but are the two equations dimensionally same? As one of them has speed of light in the denominator. $\endgroup$ Apr 22, 2022 at 16:29

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