Write equation of magnetic field due to circular current carrying loop at a point on the axis of the loop. Give its special cases.

Explanation

1. Magnetic field `vecB` due to I current carrying wire with R radius at a x distance is given by
`B=(mu_(0)IR^(2))/(2(x^(2)+R^(2))^(3//2))`
2. Case 1 : When number of turns are N, then magnetic field is `B=(mu_(0)NIR^(2))/(2(x^(2)+R^(2))^(3//2))`
3. Case 2 : Magnetic field at centre with N turn B = `(mu_(0)NI)/(2R)`
4. Case 3 : When `xgtgtR`, then `B=(mu_(0)NIR^(2))/(2x^(3))`
5. Case 4 : At x = R distance from centre,
`B=(mu_(0)NIR^(2))/(2(R^(2)+R^(2))^(3/2))=(mu_(0)NI)/(2^(5/2)R)`