Application of Magnetic Scalar Potential

Equivalence of a small current loop and a magnetic dipole

Consider a small current loop of area S carrying current l. Let p be a point having position vector r relative to centre of loop. Then
        Magnetic scalar potential at P} = V_m =μ₀I/4π Ω
Here Ω = solid angle subtended by current loop at P

        = S.r /r³ = S cos θ/r²
. :     V_m  μ₀l/4π S cos θ/r² = μ₀ /4π (IS) cos θ/r²

The expression is similar to that for potential due to electric dipole
        V = 1/4πε₀     p cos θ/r²

Thus, magnetic field due to a small current loop is similar to electric field of an electric dipole.
The produce (IS) is called magnetic dipole moment,
            m = IS

Thus, a current loop of area S carrying current I is equivalent to a magnetic dipole of dipole moment m = IS.

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