Ampere's Law for current carrying wire

In summary, using Ampere's Law, you can show that the equation for the magnetic field inside a current carrying wire is (1/2)μJr, where J is the current density and r is the radius of the wire. This is derived from the equation ∫B*ds=μI, where B is the magnetic field, s is the distance, and μ is the permeability constant. By integrating B*ds, you can arrive at ∫Bds=μJr. The limits of integration would be 0 to 2pi, treating the wire as a cylinder. J is the current per cross-section area, not a substitution for I.
  • #1
btpolk
38
0

Homework Statement



Use Ampere's Law to show that the equation for the magnetic field inside a current carrying wire is (1/2)μJr where J is the current density (assumed constant).


Homework Equations



∫B*ds=μI

The Attempt at a Solution



∫B*ds=μI

B*ds=B(ds)cosθ I think θ is 0 in this situation?

∫Bds=μI I believe r is length. If so would I=Jr?

∫Bds=μJr

From here I don't know what to do. What would my limits of integration be?
 
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  • #2
hi btpolk! :smile:
btpolk said:
I believe r is length. If so would I=Jr?

no, r is radius

and J is the current per cross-section area
 
  • #3
That said, I'm guessing I would treat the wire as a cylinder and the limits of integration would be 0 to 2pi? Also where does the J come in? Would it be some kind of substitution for I?
 

FAQ: Ampere's Law for current carrying wire

What is Ampere's Law for current carrying wire?

Ampere's Law states that the magnetic field around a current-carrying wire is directly proportional to the current passing through the wire and inversely proportional to the distance from the wire.

How is Ampere's Law used in scientific research?

Ampere's Law is used to calculate the magnetic field strength in various situations, such as around a wire or a coil of wire. It is essential in understanding the behavior of electromagnetic fields and their interactions with other objects.

What are the units for the constant of proportionality in Ampere's Law?

The constant of proportionality in Ampere's Law is known as the permeability of free space and is denoted by the symbol μ0. Its units are tesla meters per ampere (Tm/A) or newtons per ampere squared (N/A2).

What is the difference between Ampere's Law and Biot-Savart Law?

While both laws relate to the magnetic field created by current-carrying wires, Ampere's Law is used to calculate the magnetic field at points that are far away from the wire, while Biot-Savart Law is used for points that are close to the wire.

Can Ampere's Law be applied to non-linear circuits?

No, Ampere's Law can only be applied to linear circuits where the current is constant. In non-linear circuits, the current can vary, and therefore, the magnetic field cannot be calculated using this law.

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