Help with ampere's law problem

In summary, the conversation revolves around a problem involving Ampere's law for a hollow wire with inner radius a and outer radius b, carrying a current I. The first question asks for the current density in the wire, which is determined to be current per unit area. The next question inquires about the magnetic field, B(r), at different distances from the center of the wire: r < a, a < r < b, and r > b. The person providing help is unsure if their answers are correct but suggests looking into the concept of a solenoid for the second question and believes there is a magnetic field outside the wire.
  • #1
Pepsi24chevy
65
0
urgent help with ampere's law problem

The problem reads as: Consider a hollow wire of inner radius a and outer radius b carrying a current I. Use Ampere's law to find the magnitude of the magnetic field B(r) as a function of distance r from the center of the wire.

A) What is the current density in the wire?

B) What is B(r) in the center hollow of the wire (r < a)?

C) What is B(r) inside the metal part of the wire (a < r < b)?

D) What is B(r) outside the wire (r > b)?

HEre is the diagram:http://www.mustangmods.com/data/16002/untitled1.jpg

Here is my work, i don't believe i am doing it right for what it is asking.
http://www.mustangmods.com/data/16002/image15.jpg
 
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  • #2
can anyone help?
 
  • #3
I wish I could help but magnetism isn't a strong point of mine. What I can tell you is this helped me a lot last semester when I was taking the course.

A) Current density is current per unit area, your unit area here is [itex] \pi (b^2-a^2) [/itex]

B) In a solenoid there is a magnetic field between, but I'm not sure for a cylindrical wire.

C) If there was a magnetic field inside the wire, it would affect the flow of current drastically. I doubt there is one.

D) I'm quite confident there is a magnetic field outside.


Again, don't bet on my answers, but I hope it gives you some pointers until someone else helps/
 

1. What is Ampere's Law and what does it represent?

Ampere's Law is a fundamental law in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. It represents the relationship between electric currents and magnetic fields.

2. How do I apply Ampere's Law to solve problems?

To apply Ampere's Law, you first need to identify the closed loop or path where the magnetic field is being calculated. Then, you need to determine the electric current passing through the loop and the direction of the current flow. Finally, use the mathematical formula of Ampere's Law to calculate the magnetic field at the chosen point on the loop.

3. What are the units of Ampere's Law?

The units of Ampere's Law depend on the units used for electric current and magnetic field. In the SI system, the units of electric current is ampere (A) and the units of magnetic field is tesla (T). Therefore, the units of Ampere's Law are given as A/m, where A is the electric current and m is the distance from the current.

4. Can Ampere's Law be used for non-closed loops?

No, Ampere's Law can only be used for closed loops or paths. This is because the law is derived from the principle of conservation of energy, which applies to closed systems. For non-closed loops, other laws such as Biot-Savart Law or the Right-Hand Rule can be used to calculate the magnetic field.

5. What are some real-life applications of Ampere's Law?

Ampere's Law has many practical applications, including the design of electromagnetic devices such as motors, generators, and transformers. It is also used in the study of magnetic fields in different materials and in the development of magnetic sensors. Additionally, Ampere's Law is fundamental in understanding the behavior of charged particles in particle accelerators and in the study of astrophysical phenomena such as magnetic fields in stars and galaxies.

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