Ampere's Law vs Biot-Savart arouns a Square

In summary, the problem involves finding the magnitude and direction of the magnetic field at the center of a square loop conductor with a given current. While it is possible to use Ampere's Law to solve the problem, it is not applicable in this case due to the assumption of uniform B field and inability to calculate the line integral. The correct solution can be found using the Biot-Savart law.
  • #1
teroenza
195
5

Homework Statement


A conductor in the shape of a square loop of edge length l = 0.360 m carries a current I = 10.0 A. Calculate the magnitude and direction of the magnetic field at the center of the square.


Homework Equations


∮B⃗ ⋅dr⃗ =μ0 Ienclosed Ampere's Law

B=μ04π ∫I dl⃗ ×rˆr2 Biot-Savart


The Attempt at a Solution



I have seen the solution and gotten the correct answer using the formula for the B field surrounding a long, thin, conductor, derived from the Biot-Savart law.
B=(mu_0*I)/(2*pi*a) , where a is the distance from the wire to point in question.
My question is why is not possible to use Ampere's law to solve this problem. I am still in the process of tying to learn/understand Ampere's law.

Thank you
 
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  • #2
teroenza said:
My question is why is not possible to use Ampere's law to solve this problem. I am still in the process of tying to learn/understand Ampere's law.

How would you use Ampere's Law?

ehild
 
  • #3
By taking the closed line integral around the square, but that would enclose no net current. If I took the closed path for the line integral to be around the wire perpendicular to the current flow I get the same formula as that derived from Biot-Savart. However I then can't then seem to take into account the 4 lengths.
 
  • #4
When we use Ampere's Law to calculate the magnetic field around an infinite line of current we assume that B is tangential to the integration path (a circle) and uniform in magnitude. It is not valid in this case. You do not know B, it is certainly different inside the loop and outside, so you cannot calculate the line integral.

ehild
 
  • #5
Thank you very much.
 

1. What is Ampere's Law and Biot-Savart Law?

Ampere's Law and Biot-Savart Law are two fundamental laws in electromagnetism that describe the relationship between the magnetic field and the electric current in a given space.

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

The main difference between Ampere's Law and Biot-Savart Law is that Ampere's Law is used to calculate the magnetic field created by a steady current, while Biot-Savart Law is used to calculate the magnetic field created by a moving charge or changing current.

3. How do Ampere's Law and Biot-Savart Law apply to a square loop?

Both laws can be applied to a square loop by using the principle of superposition, which states that the total magnetic field at any point is the sum of the magnetic fields created by each segment of the loop.

4. Which law is more accurate for calculating the magnetic field around a square loop?

Biot-Savart Law is generally considered more accurate for calculating the magnetic field around a square loop, as it takes into account the distance between the current element and the point of interest, while Ampere's Law assumes that the current element is infinitely thin.

5. Can Ampere's Law and Biot-Savart Law be used interchangeably?

No, Ampere's Law and Biot-Savart Law cannot be used interchangeably as they are based on different assumptions and are applicable in different scenarios. However, in certain cases where the current distribution is symmetric, both laws can yield the same result.

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