Finding magnetic flux density from magnetization vector

In summary, the task is to find the magnetic flux density inside and outside a long cylinder of radius a with magnetization vector M=M_0*(r/a)^2*a_φ. This can be done by computing the integrals for ∇ x M and M x an, and then inserting them into the equations for A and B. The challenge lies in dividing the problem between the inside and outside of the cylinder, and in computing the integrals.
  • #1
moeidur
1
0

Homework Statement


A long cylinder of radius a with magnetization vector M=M_0*(r/a)^2*a_φ. Find the magnetic flux density inside and outside the cylinder.

Homework Equations


J_m=∇×M
J_ms=M×a_n[/B]
A=(μ_0/4*π)*(∫(J_m/R)dv+∫(J_ms/R)ds)
B=∇×A

The Attempt at a Solution


Basicly what I thought I'd do is find J_m and J_ms and insert that into A equation and then insert A into B equation. My main problem is I'm not sure how to compute the integrals and also not sure how to divide the problem between inside and outside the cylinder.
 
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  • #2
Welcome to PF!

Can you get explicit expressions for ∇ x M and M x an? That might help you see how to proceed.
 

Related to Finding magnetic flux density from magnetization vector

1. What is magnetic flux density?

Magnetic flux density, also known as magnetic induction or magnetic field strength, is a measure of the strength of a magnetic field at a given point. It is represented by the symbol B and is measured in units of tesla (T) or gauss (G).

2. How is magnetic flux density related to magnetization vector?

Magnetic flux density is directly proportional to the magnetization vector, which is a measure of the magnetic dipole moment per unit volume of a material. The relationship between the two is described by the equation B = μH, where μ is the permeability of the material and H is the magnetization vector.

3. Can magnetic flux density be measured?

Yes, magnetic flux density can be measured using a device called a magnetometer. Magnetometers use sensors to detect changes in the magnetic field and convert them into measurable values. They are commonly used in scientific research and in industries such as geology, navigation, and materials testing.

4. How is magnetic flux density calculated from a magnetization vector?

To calculate magnetic flux density from a magnetization vector, you can use the equation B = μH, where B is the magnetic flux density, μ is the permeability of the material, and H is the magnetization vector. In some cases, the material may have a constant permeability and the equation can be simplified to B = μ0M, where μ0 is the permeability of free space and M is the magnetization vector.

5. What factors can affect the calculation of magnetic flux density from a magnetization vector?

The calculation of magnetic flux density from a magnetization vector can be affected by factors such as the material's permeability, its shape and size, and the presence of external magnetic fields. It is important to consider these factors when conducting experiments or making calculations to ensure accurate results.

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