Find the magnetic field B at the centre of a rectangular loop of length ℓ and width b, carrying a current i.
Let us consider two angles made by points A and B with point O be θ1 and θ2 respectively.
θ1 = θ2 = θ
Let distance of the point from the wire
In triangle
Thus induced magnetic field due to AB is given by,
⇒
⇒
⇒
Similarly the induced magnetic field due to current in BC is given as:
Now, magnetic field due to CD = magnetic field due to current in wire AB =B
Also, magnetic field due to current in wire DA = magnetic field due to current in wire BC =B’
∴