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?

Explanation

Magnetic field due to loop at its centre
`B = (mu_oi)/(2pi)`
To vanish above magnetic field we place a
straight wire of 4i curretn at a distance x
such that their magnetic fields directions
be opposite.
Thus `(mu_oi)/(2pi) = (mu_o4i)/(2pix)`
`rArr x = (8r)/(2pi) = (4r)/(pi)`
i.e. wire is placed`(4r)/(pi)` from the centre of
the loop.