How does self inductance of coil or solenoid vary with its area of cross section?
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The self inductance of a coil is L=NIϕ where N= number of turns on coil, A= cross section area and I= current passes through coil.
Now, ϕ=BA=(lμ0NI)A where B= magnetic field inside the solenoid and l= length of the solenoid.
Thus, L=μ0lN2A
So, L′=μ0(2l)(2N)2A=2μ0lN2A=2L
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