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## Homework Statement

One solenoid is centered inside another, The outer one has a length of 50cm and has 6750 coils, while the coaxial inner solenoid is 3cm long and 0.12cm in diameter and contains 15 coils. What is the mutual inductance of these solenoids?

## Homework Equations

M=N

_{1}[tex]\phi[/tex]

_{1}/I

_{2}

M=N

_{2}[tex]\phi[/tex]

_{2}/I

_{1}

Note: 1 refers to the outer loop and 2 the inner loop.

## The Attempt at a Solution

I used both the above equations. One way is to find the B

_{1}due to the outer solenoid, multiply that B

_{1}by the area of the inner solenoid to get the flux through coil of the inner solenoid, [tex]\phi[/tex]

_{2}. Then use the second equation. But that answer which is (2.8*10^-7)H is incorrect.

Then I tried multiplying B

_{2}with the area of the inner solenoid again to get [tex]\phi[/tex]

_{1}. Then I used the first equation to get the answer which is (4.8*10^-6)H and this is correct.

Why is the first method wrong? This seems to be giving me two different values for the mutual inductance between two coils. Thank you for your help! If it helps, this is taken from the textbook University Physics by Young and Freedman. It is problem 30.43 in edition 12.

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