Potential Energy of a Magnetic Moment

Let us consider a charge with its charge density of p which moves at its velocity of v as shown in Fig. 1-3. In this case, its current density (j) becomes 

the force (f) induced to this unit volume by a magnetic field of B is given from Eq. (1-5) by 

When the cross section of this wire is S, the force (dF) induced to the wire with its length of dL becomes as follows  

Because the total current of this wire (I) is 5j, dF can be represented as 

Then let us consider the forces induced by B to a rectangular coil (a x b) with a current of / as shown in Fig. 1-4. 

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The potential energy of a magnetic moment in a magnetic field can be calculated according to the recipe given in Section 1.4.5. Taking into account that in this case Mp is the moment of external forces, we obtain... 

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