Magnetic Flux in a Coaxial Cable

In summary, the magnetic flux through a coaxial cable only includes the magnetic field generated by the current flowing through the center conductor, not the outer conductor. This is due to Ampere's law in integral form and the radial symmetry of a circular cross section. Since there is no current passing through the outer conductor, the magnetic field is zero. Additionally, the motion of the moving electrical charges in the z-direction and the divergence of the magnetic field also contribute to the cancellation of the magnetic field from the outer conductor.
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Drakkith
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Let's say we have a coaxial cable with a 2d rectangular surface lying between the inner and outer conductors and running the length of the cable. I'm trying to understand why the magnetic flux through this surface only includes the magnetic field generated by the current flowing through the center conductor and not the outer conductor. I'm assuming the fields from the current running through the outer conductor cancel out somehow. Is it just that simple?
 
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Ampere's law in integral form is perhaps the easiest way to show the magnetic field from the outer conductor is zero. A circular cross section works best, so that the radial symmetry can be applied. Ampere's law in integral form says: ## \oint B \cdot dl =\mu_o I ## where ## I ## is the current through the loop and the integral is around the loop. If there is no current passing through the circular loop (from the outer conductor), by symmetry ## B=0 ##. (At least the tangential component.) Meanwhile, ## B_z=0 ## because the motion of the moving electrical charges is in the z-direction. (by Biot-Savart's law, the ## v \times r ## in the numerator of the Biot-Savart equation for ## B ## tells us that any ## B ## will be perpendicular to ## v ##. Finally ## B_r=0 ## can be shown by using ## \nabla \cdot B=0 ## along with Gauss's law.
 
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1. What is magnetic flux in a coaxial cable?

Magnetic flux in a coaxial cable refers to the amount of magnetic field passing through the cable's cross-sectional area. This magnetic field is generated by the electric current flowing through the cable.

2. How is magnetic flux measured in a coaxial cable?

Magnetic flux in a coaxial cable is measured in units of webers (Wb) or teslas (T). It can also be measured indirectly by using a gaussmeter to measure the strength of the magnetic field surrounding the cable.

3. Why is magnetic flux important in a coaxial cable?

Magnetic flux is important in a coaxial cable because it affects the cable's performance and can cause interference with other electronic devices. Excessive magnetic flux can lead to signal distortion and loss of data, while low magnetic flux can result in a weak signal and poor transmission.

4. How does the geometry of a coaxial cable affect magnetic flux?

The geometry of a coaxial cable, specifically the distance between the inner and outer conductors, can affect the amount of magnetic flux present. A smaller distance between the conductors will result in a stronger magnetic field and therefore a higher magnetic flux.

5. Can the magnetic flux in a coaxial cable be controlled?

Yes, the magnetic flux in a coaxial cable can be controlled by using materials that have high magnetic permeability, such as iron or ferrite, to shield the cable from external magnetic fields. Additionally, using twisted pairs or braided shielding can also help reduce the effects of magnetic flux on the cable's performance.

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