A square loop of wire, edge length a, carries a current i. Compute the magnitude of the magnetic field produced at a point on the axis of the loop at a distance x from the centre.
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Sol. A point on the axis of the loop is on the perpendicular bisector of each of the loop sides. The figure shows field of a single wire.
B = 
When the fields of all the four sides are considered, the horizontal components add to zero; so the total field is given by
B R = 4Bcos θ = 
= 
= 
For x = 0 the expression reduces to
B R = 
= 
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