- #1

asap9993

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## Homework Statement

A small, thin coil with N

_{2}loops, each of area A

_{2}, is placed inside a long solenoid, near its center. The solenoid has N

_{1}loops in its length L and has area A

_{1}. Find the mutual inductance as a function of θ, the angle between the plane of the small coil and the axis of the solenoid.

## Homework Equations

M

_{2}= N

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

_{2}/I

_{1}

[itex]\phi[/itex]

_{2}= BA

_{2}cos(θ) = μ

_{0}(N

_{1}/L)I

_{1}A

_{2}cos(θ)

## The Attempt at a Solution

If we just substitute for [itex]\phi[/itex]

_{2}into the equation for M

_{2}, we get that

M

_{2}= (N

_{2}/I

_{1})BA

_{2}cos(θ) = μ

_{0}(N

_{1}N

_{2}/L)A

_{2}cos(θ)

Everything is right here except that the correct solution has sin(θ) instead of cos(θ). Why is that? Isn't the magnetic flux defined as a dot product?