# Solved Problems-18

Problem-18
An infinite straight wire carrying a current I is placed to the left of a rectangular loop of wire with width and length l, as shown in . Determine the mutual inductance of the system.
Rectangular loop placed near long straight current-carrying wire

Solution
To calculate the mutual inductance M, we first need to know the magnetic flux through the rectangular loop. Using Ampereâ€™s law, the magnetic field at a distance r away from the straight wire is given as,

The total magnetic flux φ through the loop can be obtained by summing over contributions from all differential area elements  as follows.

Hence, the mutual inductance is given as,