Question

A circular loop of radius r carries a current i. How should a long, straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the centre becomes zero?

Answer 1

vector B due to loop μ₀i/2r

Let the straight current carrying wire be kept at a distance R from centre. Given I = 4i

Hence the straight wire should be kept at a distance 4π/r from centre in such a way that the direction of current in it is opposite to that in the nearest part of circular wire. As a result the direction will vector B will be oppose.