Magnetic flux between coaxial conductors

[einarbmag]

Homework Statement

A coaxial conductor has the length L. The inner conductor of radius a carries a
current I in the z direction. The outer conductor is very thin and has the radius
b. Calculate the total magnetic flux enclosed within the conductors.

Homework Equations

Magnetic flux around a cylindrical conductor: B_(phi)=(mu_0)*I/(2*pi*r)

The Attempt at a Solution

The question really is whether the outer conductor does anything except determine the region where the flux is to be calculated. Is the outer conductor affected at all since the magnetic flux density from the inner conductor isn't changing, and does it then have any effect on the flux?

 

[jhicks]

and does it then have any effect on the flux?

Nope

 

[Moetasim]

I would approach this problem by first considering the basic principles and equations involved. The equation for magnetic flux around a cylindrical conductor, given above, is applicable here. However, in this case, we have two concentric conductors, and the magnetic flux will be enclosed between them.

To calculate the total magnetic flux, we need to consider the magnetic field created by the current in the inner conductor and the area enclosed between the two conductors. The area in this case will be the annular region between the two conductors, with inner radius a and outer radius b.

Using the equation for magnetic flux, we can calculate the flux at each point within this annular region and then integrate over the entire area to get the total flux.

However, as the question mentions, the outer conductor is very thin and has a small radius b. This means that the magnetic flux density created by the current in the inner conductor will be significantly larger than the flux density created by the current in the outer conductor. Therefore, the contribution of the outer conductor to the total magnetic flux will be negligible.

In this case, the total magnetic flux will be primarily determined by the current in the inner conductor and the area enclosed between the two conductors. The outer conductor, although present, will not have a significant effect on the total magnetic flux.

In conclusion, the total magnetic flux between coaxial conductors can be calculated by considering the magnetic field created by the current in the inner conductor and the area enclosed between the two conductors. The outer conductor, while present, will not have a significant effect on the total magnetic flux.