# Magnetic flux between coaxial conductors

• einarbmag
The total magnetic flux enclosed within the conductors is simply the magnetic flux around the inner conductor, which can be calculated using the formula B_(phi)=(mu_0)*I/(2*pi*r). Therefore, the total magnetic flux is directly proportional to the current I and inversely proportional to the radius a. In summary, the magnetic flux enclosed within a coaxial conductor with an inner conductor of radius a carrying a current I is given by B_(phi)=(mu_0)*I/(2*pi*a).
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?

einarbmag said:
and does it then have any effect on the flux?

Nope

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.

## 1. What is magnetic flux?

Magnetic flux is a measure of the strength of a magnetic field passing through a certain area. It is represented by the symbol Φ and is measured in units of webers (Wb).

## 2. How is magnetic flux calculated?

Magnetic flux is calculated by multiplying the strength of the magnetic field (B) by the area (A) that the field passes through, and then taking the cosine of the angle between the field and the area. This can be represented by the equation Φ = B*A*cos(θ).

## 3. What is the difference between magnetic flux and magnetic flux density?

Magnetic flux and magnetic flux density are related but different concepts. Magnetic flux is a measure of the total amount of magnetic field passing through a certain area, while magnetic flux density (B) is a measure of the strength of the magnetic field at a specific point in space.

## 4. How does magnetic flux change between coaxial conductors?

Magnetic flux between coaxial conductors is dependent on the distance between the conductors, the current flowing through them, and the permeability of the materials. As the distance between the conductors increases, the magnetic flux decreases. Similarly, as the current or permeability increases, the magnetic flux also increases.

## 5. What is the significance of magnetic flux between coaxial conductors?

Magnetic flux between coaxial conductors is important in understanding and designing electrical circuits, particularly in applications involving transformers and inductors. It also plays a role in the transmission and distribution of electricity.

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