Ampère's circuital law and finite conductor

In summary, the conversation discusses the use of Ampère's circuital law to find the electric field for a finite current carrying conductor at a point away from it. It is stated that the law can be used, but there is a discrepancy between the length of the wire and the resulting field, making it unreliable. It is also mentioned that the Biot-Savart law can be used anytime, as it is derived from Ampère's law. The conversation ends with a clarification that the Ampère's law being referenced does not include the displacement current correction.
  • #1
vijender
1
0
Can Ampère's circuital law be used to find electric field for a finite (say length l) current carrying this conductor at a finite point away from it?
If yes, then what will be Magnetic field due to a wire extending from (0,-a/2) to (0,a/2) carrying current “I” at a point (b,0) from it, if I consider a loop (circle here) of radius b/2 perpendicular to the x-axis centered at origin?
 
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  • #2
Yes. You can consider a infinitesimal current element and the resulting field. Then you integrate across the strength and length of your current. This has already been derived easily by most textbooks in the form of say the Biot-Savart Law for magnetostatics.
 
  • #3
No, ampere's law can't be used here. You can always change the length of the wire and get the same answer. This absolutely can't be true
The derivation of Ampere's law requires that [tex]\nabla.J=0[/tex] everywhere. On the other hand Biot-Savart can be used anytime
 
  • #4
EHT said:
No, ampere's law can't be used here. You can always change the length of the wire and get the same answer. This absolutely can't be true
The derivation of Ampere's law requires that [tex]\nabla.J=0[/tex] everywhere. On the other hand Biot-Savart can be used anytime

Biot-Savart is derived from Ampere's Law. Ampere's Law does not make any conditions upon the divergence of the current. When we talk about Ampere's Law, we are talking about the Ampere's Law as it appears in Maxwell's Equations.

Thus, the OP can use Ampere's Law (along with other Maxwell Equations) to derive the Biot-Savart Law for an infinitesimal current element (moving charge with constant velocity which thus requires a non-zero divergence in the current). Then the OP can use this as the basis for his contour integral around his arbitrarily shaped current loop as he has described previously.
 
Last edited:
  • #5
as in the other thread, the ampere law that I mentioned is the one without displacement current correction in it
 

1. What is Ampère's circuital law and what does it state?

Ampère's circuital law is a fundamental law in electromagnetism that describes the relationship between the electric current flowing through a conductor and the resulting magnetic field. It states that the line integral of the magnetic field around a closed path is equal to the product of the current passing through the surface enclosed by the path and a constant called the permeability of free space.

2. How does Ampère's circuital law apply to finite conductors?

Ampère's circuital law can be applied to finite conductors by breaking the conductor into small segments and using the law to calculate the magnetic field produced by each segment. The total magnetic field is then found by summing the contributions from each segment using vector addition.

3. What is the significance of Ampère's circuital law in practical applications?

Ampère's circuital law is crucial in understanding and predicting the behavior of magnetic fields in various practical applications, such as designing electric motors, generators, and transformers. It also helps in analyzing the behavior of electromagnetic waves and the creation of magnetic fields in different materials.

4. How does Ampère's circuital law relate to Gauss's law for electricity?

Ampère's circuital law and Gauss's law for electricity are both laws that describe the relationship between an electric field and its source. Ampère's law deals with the relationship between a magnetic field and its source (electric current), while Gauss's law deals with the relationship between an electric field and its source (electric charge).

5. Are there any limitations to Ampère's circuital law?

Yes, Ampère's circuital law is only applicable to steady currents and does not account for time-varying currents. It also assumes that the magnetic field is constant and does not account for changing electric fields. In some cases, this law may not accurately predict the behavior of magnetic fields, and more advanced principles, such as Maxwell's equations, must be used.

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