(a) Draw the pattern of magnetic field lines for a circular coil carrying current.
(b) Two identical planes such that they have a common centre at P as shown in the figure. Find the magnitude and direction of the net magnetic field at the point P due to the loops

Explanation

(a) Magnetic field lines of a current carrying coil.
Point O lies on the axis of both the coils. Magnetic field at O due to current carrying coil I is given by `(mu_(0))/(4pi) xx (2pi I R^(2))/((R^(2) + x^(2))^(3//2))` as shown
Also `B_(2)` due to coil `2, B_(2) = (mu_(0))/(4pi) (2pi iR^(2))/((R^(2) + x^(2))^(3//2)) " as " B_(1) and B_(2)` are perpendicular each other, so net magnetic to field at O is given by
`B = sqrt(B_(1)^(2) + B_(2)^(2)) = sqrt2B_(1) = sqrt2 ((mu_(0))/(4pi)) (2pi R^(2))/((R^(2) + x^(2))^(3//2))`
`:. B_(1) = B_(2)`