The question is: How can I find the magnetic field inside a long conductor?

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In summary, The problem involves finding the magnetic field inside a long conductor with cylindrical symmetry using Ampere's law. The equation used is ∫B.dl=μIenclosed and the direction of the magnetic field is along θ. The fraction of current inside the area considered is found using the equation ∏r2/∏a2 and the current density is assumed to be evenly distributed across the cross-sectional area of the wire. The final equation is Ienc/∏r2= Itotal/∏α2.
  • #1
humanist rho
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Homework Statement


I have to find the magnetic field inside a long conductor of radius a.


Homework Equations


Ampere's law.
∫B.dl=μIenclosed


The Attempt at a Solution



Problem has cylindrical symmetry and B is along θ direction.

B*2∏r=μIenclosed

How to find what fraction of current inside the area considered?

I just saw in a book that it is ∏r2/∏a2.But can't figure out the idea.:(

I know it is very simple and donno why i forget basics always..:(
 
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  • #2
You have a total current I in the wire. Assume it's evenly distributed across the cross-sectional area of the wire. What would be the current density?
 
  • #3
Yeah!now got it.
Current density is constant.

Ienc/∏r2= Itotal/∏α2
 

FAQ: The question is: How can I find the magnetic field inside a long conductor?

1. What is Ampere's Law?

Ampere's Law is a fundamental law in electromagnetism that describes the relationship between electric currents and magnetic fields.

2. Who discovered Ampere's Law?

Ampere's Law was discovered by French physicist André-Marie Ampère in the early 19th century.

3. What does Ampere's Law state?

Ampere's Law states that the magnetic field created by an electric current is directly proportional to the magnitude of the current and the distance from the current.

4. How is Ampere's Law used in practical applications?

Ampere's Law is used in many practical applications, such as designing electromagnets, motors, and generators. It is also used in medical devices like MRI machines and particle accelerators.

5. Are there any limitations to Ampere's Law?

While Ampere's Law is a fundamental law in electromagnetism, it has its limitations. It does not take into account the effects of changing electric fields and is only applicable to steady currents. It also does not account for the effects of magnetic materials.

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