Obtain an expression for magnetic field in terms of magnetic dipole moment associated with circular current loop.
`" "`(or)
Show that circular current loop can be associated with a magnetic dipole.

Explanation

We know that the magnetic field at a point on the axis of a circular loop.
`" "B=(mu_(0)/(4pi))(2piIR^(2))/(x^(2)+R^(2))^(3/2)` R - radius of the loop.
For a distance `" x>>R", x^(2)+R^(2)=x^(2)`
and `" "(x^(2)+R^(2))^(3/2)=x^(3)`
Hence, `" "B=(mu_(0)/(4pi))(2piIR^(2))/(x^(3))" where", piR^(2)=A` (area of circular loop)
i.e., `" "B=(mu_(0)/(4pi))(2IA)/(x^(3))" where", m=IA=` magnetic moment
Hence,`" "vec(B)=(mu_(0)/(4pi))(2vec(m))/(x^(3))" ...(1)"`
Hence circular loop acts as a magnetic dipole.
Note :
`*` As an analogous to the electric field intensity
`" "vec(E)=(1/(4piepsilon_(0)))(2vec(p)_(e))/(x^(3)) " ...(2)"`
`*` Comparing (1) and (2) we note that by substituting `mu_(0) " as " 1/epsilon_(0)`
and `vec(B)` by `vec(E), vec(m) " by " vec(p)_(e)`, one can relate the magnetic and electric fields due to the corresponding dipoles.