A circular loop of radius R carrying a current I lies in the x-y plane with its centre at the origin. A long straight wire carrying the same current I is placed parallel to the y -axis, passing through the point (d, 0, 3 R) . If the net magnetic field at the point (0, 0, 3 R) is zero, then the distance d is:

Step-by-step solution

The point of interest is P(0, 0, 3 R) , which lies on the axis of the circular loop. The magnetic field produced by the circular loop at point P is directed along the z -axis and its magnitude is: B_ loop = ₀ I R² 2(R² + ( 3 R)²)^ 3/2 = ₀ I R² 2(4R²)^ 3/2 = ₀ I 16R The long straight wire is parallel to the y -axis and passes through (d, 0, 3 R) . The shortest distance from the point P(0, 0, 3 R) to this wire is along the x -axis, which is equal to d . The magnetic field produced by the straight wire at point P is: