A uniform conducting wire of length 12a and resistance ‘R’ is wound up as a current carrying coil in the shape of,

(i) an equilateral triangle of side ‘a’.

(ii) a square of side ‘a’.

The magnetic dipole moments of the coil in each case respectively are :

Concept:

Magnetic dipole moment is associated with magnetic dipole, Current carrying conductors etc. It is vector quantity and is equal to amount of electric current in the wire multiplied by the area of the loop.

The strength of the magnet or the magnetic dipole moment is represented by the equation:

M = NIA

Where M represents magnetic dipole moment.

Calculation:

Current in the loop will be \(\frac{V}{R} = I\) which is same for both loops.

Now magnetic moment of Triangle loop = NIA

\({M_1} = \left( {\frac{{12a}}{{3a}}} \right).I.\frac{{\sqrt 3 }}{4}{a^2} = \sqrt 3 l{a^2}\)

and magnetic moment of square loop = N'IA'

\( = \left( {\frac{{12a}}{{4a}}} \right).I.{a^2}\)

M₂ = 3la²