B field inside conductor with assymetric cavity

In summary, the conversation discusses finding the direction and magnitude of the B-field inside a cylindrical cavity in an infinite straight conductor with a current flowing through it. The suggested approach is to use the equation \oint \textbf{B} \cdot \textbf{dl} = \mu _0 I and subtract the inner line integral from the outer line integral.
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Gauss M.D.
153
1

Homework Statement



Infinite straight conductor, parallel with z axis, of radius R1 with a cylindrical cavity of radius R2. The axis of the cavity passes through the point <0,b,0>. A current I flows through the conductor. The current density is homogenous inside the cundoctor. Find the direction and magnitude of the B-field inside the cavity.

Homework Equations





The Attempt at a Solution



I think we're supposed to use

[itex]\oint \textbf{B} \cdot \textbf{dl} = \mu _0 I[/itex]

Where we first do the outer line integral, and then subtract the inner line integral.

1) Am I on to something?
2) How do I do the inner line integral in the most convenient way?
 
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FAQ: B field inside conductor with assymetric cavity

1. What is the purpose of studying the B field inside a conductor with an asymmetric cavity?

The B field inside a conductor with an asymmetric cavity is studied in order to understand the behavior of magnetic fields in complex systems. This type of study has applications in various fields such as electromagnetism, material sciences, and engineering.

2. How is the B field affected by the shape of the asymmetric cavity?

The shape of the asymmetric cavity can significantly affect the B field inside a conductor. In general, the B field will be stronger in areas where the cavity is narrower, and weaker in areas where the cavity is wider. This can result in non-uniformity in the B field distribution.

3. What factors can influence the B field inside a conductor with an asymmetric cavity?

The B field inside a conductor with an asymmetric cavity can be influenced by various factors such as the shape and size of the cavity, the material properties of the conductor, the current flowing through the conductor, and the presence of other nearby conductors or magnetic materials.

4. How is the B field inside a conductor with an asymmetric cavity measured?

The B field inside a conductor with an asymmetric cavity can be measured using a variety of techniques such as magnetic field sensors, Hall effect sensors, and magnetic field mapping tools. These measurements can provide valuable information about the behavior of the B field in the system.

5. What are some potential applications of studying the B field inside a conductor with an asymmetric cavity?

Studying the B field inside a conductor with an asymmetric cavity has many potential applications. It can help in designing efficient and uniform magnetic fields for applications such as particle accelerators, magnetic confinement fusion reactors, and magnetic resonance imaging (MRI) systems. It can also aid in understanding the behavior of magnetic fields in complex materials and systems, leading to advancements in various fields.

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