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Magnetic Field due to Circular Current

If a coil of radius r is carrying current i, then the magnetic field on it’s axis at a distance x from its center is given by (Application of Biot-Savart’s law; Fig. 13)
 
82041.png
Fig. 13
  • 81814.png; where N = number of turns in coil.
  • At center x = 0
     
    81824.png
  • The ratio of magnetic field at the center of circular coil and on its axis is given by 81830.png
  • If x >> r 81836.png
     
    where A = πr2 = area of each turn of the coil.

B–x curve

The variation of magnetic field due to a circular coil as the distance x varies as shown in Fig. 14.
 
82049.png
Fig. 14
 
B varies non-linearly with distance x as shown in Fig. 14 and is maximum when x2 = min = 0, i.e., the point is at the center of the coil and it is zero at x = ± ∞.

Point of inflection (A and A’)

Also known as points of curvature change or points of zero curvature.
  • At these points B varies linearly with x 81842.png constant 81851.png.
  • These are located at 81861.png from the center of the coil and the magnetic field at
     
    81867.png is 81873.png




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