Question

Expression for mutual inductance of infinitely long filamenary loop wire

Answer 1

Answer:

Explanation:

Let us consider a strip of width dx at a distance x from the wire carrying current magnetic field due to current carrying wire at a distance x from the wire is B=μoI2πx

small amount of magnetic flux associated with the strip is

dϕ=BdA=μoI2πx(adx)

Magnetic flux linked with the square loop

ϕ=μoIa2π∫x=a+bx=bdxx=μoIa2π[logex]a+bb=μoIa2πloge[a+bb]=μoIa2πloge[1+ab]

Since ϕ=MI∴MI=μoIa2πloge[1+ab]

⟹M=μoa2πloge[ab+1]