Magnetic field on the axis of a circular current loop | cbse24

Consider a circular loop of wire of radius a and carrying current I, as shown in figLet the plane of the loop be perpendicular to the plane of the paper. We going to find field B at an axial point P at a distance of r from the centre C

The magnetic field on the axis of a circular current loop

Consider a current element dl at the top of the loop. It has an outward coming current.

If s be the position vector of point P relative to the element dl, the Biot-savert law , the field at point P due to the current element is

dB resolved into two rectangular components.
  1. dBsinΦ along the axis
  2. dBcosΦ perpendicular to the axis
∴ The total magnetic field at the point P in the direction CP is

Since μo and I are constant, and s and a is the same for all points on the circular loop, we have

{∵ ∫ dl = circumference=2πa}

If the coil consists of N turns, then

Special Cases:

  • At the centre of the current loop, r =0, therefore
  • At the axial points lying far away from the coil, r>>a, so that
  • At the axial point at a distance equal to the radius of the coil i.e., r=a, we have


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