A very small conducting circular loop of radius r is placed in the same plane as a long straight wire. The center of the loop is at a perpendicular distance x from the wire. Given that x r , the mutual inductance M of the system is directly proportional to:

Step-by-step solution

Let the current in the long straight wire be I . The magnetic field produced by the long straight wire at a perpendicular distance x is given by B = ₀ I 2 x . Since x r , the magnetic field over the area of the small circular loop can be considered approximately uniform and equal to the value at its center. The area of the circular loop is A = r^2 . The magnetic flux passing through the loop is = B A = ( ₀ I 2 x ) ( r^2) = ₀ I r^2 2 x . The mutual inductance M is defined as the magnetic flux through the loop per un