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# (Solved): HELP WITH PROBLEM C only #3 One solenoid is centered inside another. The outer solenoid has a lengt ...

HELP WITH PROBLEM C only #3 One solenoid is centered inside another. The outer solenoid has a length of

`l_(2)=75cm`

and

`N_(2)=6750`

coils. The coaxial inner solenoid has a length

`l_(1)=12cm`

, it has

`N_(1)=1200`

coils, and is

`r_(1)=1cm`

in radius. (The figure from the intro video is shown here to give you an idea of the setup, but please notice that the values given tell us that the situation in this problem is reversed with the inner solenoid being shorter than the outer one.) (a.) Use the expression

`M=(N_(1)\Phi _(B1))/(i_(2))`

to find an equation for the mutual inductance of these solenoids. Your answer should just be an equation (so don't substitute any numerical values yet) and should include only constants and geometric factors such as

`l_(1),l_(2)`

, and

`r_(1)`

. (b.) Show that

`M=(N\Phi _(B2))/(i_(i))`

gives the same result. Hint: The number of loops here is not

`N_(2)`

. It's just how many of outer solenoid's loops overlap with the inner solenoid. Also, it is no mistake that the diameter of the outer solenoid was not given. (c.) Find the numerical value of the mutual inductance for these solenoids. (d.) If the current in outer solenoid is changing at

`80(A)/(s)`

, find the emf induced in the inner solenoid.

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