- #1

Master1022

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## Homework Statement

I was wondering if and how we can apply Ampere's Law to a transformer?

I am just thinking about the bog standard transformer with a core, primary coil, and secondary coil.

1) How do I deal with the current from both coils?

2) Do I need to think about the opposing magnetic field created by the secondary coil? - the eventual goal is to go and find the flux density and total flux...

## Homework Equations

Ampere's Law:

[tex] \oint \vec H \cdot d \vec l = I_{enclosed} [/tex]

For an efficient transformer:

[tex] I_{p} \times V_{p} = I_{s} \times V_{p} [/tex]

## The Attempt at a Solution

The main question I have is about the current enclosed. I understand that if there was 1 coil, then we would have the enclosed current as N x I. With two coils, however, do I need to worry about the fact that the currents will be in opposite directions. I know that current is treated as a scalar quantity, but it does obey some vector properties...

If I attempt to go down the route of treating current as a vector, I end up with the enclosed current being equal to 0 because:

[tex] \frac{N_p}{N_s} = \frac{I_s}{I_p} [/tex]

and thus:

[tex] N_{p} \times I_{p} = N_{s} \times I_{s} [/tex]

but with I_s in the opposite direction, so the 'enclosed current cancels out'??

What have I misunderstood to arrive at this problem? Any help is greatly appreciated.