Magnetic field due to a circular current

If a coil of radius r, carrying current i then magnetic field on it's axis at a distance x from its centre given by  ; where N = number of turns in coil.

DIFFERENT CASES

Case 1: Magnetic field at the centre of the coil

(i) At centre x = 0  => 

(ii) For single turn coil  N = 1  => 

(iii) In C.G.S.           => 

Case 2: Ratio of B_centre and B_axis

       The ratio of magnetic range at the centre of circular coil and on it's axis is given by:

(i) If   ,         

(ii) If

Case 3: Magnetic field at very small/very large distance from the centre

(i) If x >> r (very large distance)

                =>   where A = pr² = Area of each turn of the coil.

(ii) If x << r (very small distance)

=>   , but by using binomial theorem and neglecting higher power of                 

Magnetic field because of current carrying circular arc

Magnetic field at centre O

Concentric circular loops (N = 1)

(i) Concentric and Coplanar: It means both coils are in same plane with common centre

(ii) Concentric and Non-coplanar : Plane of both coils are perpendicular to each other Magnetic field at common centre

Magnetic field with respect to a straight current carrying wire: Magnetic field due to a current carrying wire at a point P which lies at a perpendicular distance r from the wire as shown is given as

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