Question

Consider two coils, with the first coil having twice as many loops as the second. Given the flux Φ though each loop of the first coil due to current in the second coil, what can be said about the flux through each loop of the second coil due to an equal current in the first coil?

Answer 1

Answer:

$\phi_{21} = \frac{\phi_{12}}{2}$

Which means that the flux through each loop of the second coil is half as much as flux through each loop of first coil.

Explanation:

The flux through each loop of the first coil due to current in the second coil is,

$\phi_{12} = \phi$

The number of loops in the first coil is

no. of loops = 2N

Total flux passing through the first coil is

$\phi_{12} = 2N\phi$

The flux through each loop of the second coil due to current in the first coil is,

$\phi_{21} = \phi$

The number of loops in the second coil is

no. of loops = N

Total flux passing through the second coil is

$\phi_{21} = N\phi$

Comparing both

$\phi_{12} = \phi_{21} \\\\ 2N\phi = N\phi\\\\\phi_{21} = \frac{\phi_{12}}{2}$

Which means that the flux through each loop of the second coil is half as much as flux through each loop of first coil.