Figure shows a rectangular coil near a long wire. Calculate the mutual inductance of the combination.
Text Solution
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Sol. Let the current i 1 in the straight wire be upward. The magnetic field due to the straight wire has magnitude B 1 = μ 0 i 1 /2 π r at a distance r. In accordance with right hand rule B 1 points inward to the plane of page. We consider a differential strip of thickness dr, area dA 2 = adr. Magnetic flux through area dA, d φ B = B 1 (adr).
Total flux through the loop,
= 
= 
adr
= 
= 
Therefore, the mutual inductance,
M = M 12 = 
= 
ln 
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