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Solved Problems-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
To calculate the mutual inductance M, we first need to know the magnetic flux through the rectangular loop. Using Ampere’s law, the magnetic field at a distance r away from the straight wire is given as,
Description: Description: 108557.png
The total magnetic flux φ through the loop can be obtained by summing over contributions from all differential area elements Description: Description: 108550.png as follows.
Description: Description: 108543.png
Hence, the mutual inductance is given as, Description: Description: 108536.png
Description: Description: 108528.png

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