How Does Ampere's Law Determine the Ranking of Loops by Enclosed Current?

In summary, the conversation is about ranking loops according to the current they enclose, with the largest current enclosed being ranked first. The equations for calculating the magnetic field for different positions around a wire are discussed, with the solution being option d and c being tied for first, followed by option b, and then option a. The concept of treating current density as uniform across the wire is mentioned, and the conversation ends with the acknowledgement that sometimes we can overthink a problem and the solution may be simpler than we initially thought.
  • #1
ZeroVersion
5
0
Hellow every one I have small Q but I stuck on it

there is pic attachedhope to be intersting and clear to you

Homework Statement


rank the loops accoroding to the current enclosed greatest first

Homework Equations



we have three eqn's
B = u "node" I encِْْْْ
B = u"node" i / 2 pi r outside the wire
B = (u"node" i / 2 pi R2 ) r inside the wire

The Attempt at a Solution

I knew the solotion but I do not know how did they get it

the soloution is d and c tie then b then a
 

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  • #2
Hint: Treat the current density as uniform across the wire.
 
  • #3
thank you very much Doc al it is as what you mentioned related to the current density for c and d the current is the same whereas in b smaller and a is even smaller than b



Sometimes we think in very difficult method when we can solve it in easier way


Thank you again and regards​
 

1. What is Ampere's law wire problem?

Ampere's law wire problem is a physics problem that involves calculating the magnetic field strength at a point due to a current-carrying wire. It is based on Ampere's law, which states that the magnetic field around a closed loop is directly proportional to the current passing through the loop.

2. How do you use Ampere's law to solve a wire problem?

To solve an Ampere's law wire problem, you first need to determine the direction of the magnetic field around the wire. This can be done by using the right-hand rule, which states that if you point your thumb in the direction of the current, your fingers will curl in the direction of the magnetic field. Then, you can use the formula B = μ0I/2πr to calculate the magnetic field strength at a given distance from the wire, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire.

3. What factors affect the magnetic field strength in an Ampere's law wire problem?

The magnetic field strength in an Ampere's law wire problem is affected by the magnitude of the current in the wire, the distance from the wire, and the permeability of the material surrounding the wire. The direction of the current also plays a role in determining the direction of the magnetic field.

4. Can Ampere's law be used to solve problems with wires of different shapes?

Yes, Ampere's law can be used to solve problems with wires of different shapes. However, the shape of the wire may affect the direction and distribution of the magnetic field, so the calculations may be more complex.

5. Are there any limitations to using Ampere's law in wire problems?

One limitation of using Ampere's law in wire problems is that it assumes that the current is constant along the entire length of the wire. In reality, the current may vary along the wire, especially if the wire is not straight. Additionally, Ampere's law is only applicable to steady currents and does not take into account any time-varying effects.

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