Application of Biot-Savart Law for Finite Wire: Exploring Point P and P_1

In summary, the conversation is about the application of the Biot-Savart law along a finite wire. The question is whether the equation defining the magnetic field in point P(x,y) also applies to the point P_1(x,y), which is not within the boundaries of the wire. The person answering the question confirms that the equation does apply, but emphasizes the importance of defining x correctly when applying the law. The conversation ends with the suggestion of defining x as x=L/2 + x_1.
  • #1
czmat
Hi,
I've got a question regarding application of the Biot-savart law along finite wire.
There is a great explenation of this problem in the MIT paper but this does not cover one case.

1. Homework Statement
My question is: does the equation defining magnetic field in point P(x,y) also applies to the point P_1(x,y) (as in the picture below) which is not in boundaries of the wire?
inFOYwS.jpg


Homework Equations


Magnetic field in point P(x,y) (as in the above figure) along finite wire is:
BT5SBz7.jpg

The Attempt at a Solution


My guess is: yes, just because I can put P_1 coordinates in the equation, but intuition tells me that I am omitting something and unfortunately I don't know what.
 
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  • #2
czmat said:
My question is: does the equation defining magnetic field in point P(x,y) also applies to the point P_1(x,y) (as in the picture below) which is not in boundaries of the wire?
Yes, but you have to be careful with how you apply Biot-Savart, specifically what is x. You are omitting x1 from the picture.
 
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  • #3
In that case I would define x as
x=L/2 + x_1
 
  • #4
Yes.
 
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1. What is the Biot-Savart Law?

The Biot-Savart Law is a fundamental law in electromagnetism that describes the magnetic field produced by a current-carrying wire at a given point in space. It states that the magnetic field at a point is directly proportional to the current in the wire, the length of the wire, and the sine of the angle between the wire and the line connecting the point to the wire.

2. How is the Biot-Savart Law applied to a finite wire?

The Biot-Savart Law can be applied to a finite wire by breaking the wire into small segments and calculating the magnetic field contribution from each segment at the point of interest. This process is repeated for all segments, and the total magnetic field is calculated by summing up the contributions from each segment. This allows us to account for the varying angles and distances between the wire segments and the point of interest.

3. What is the significance of exploring point P and P_1 in relation to the Biot-Savart Law for finite wire?

Point P and P_1 represent two different points in space where the magnetic field is being calculated. By exploring the behavior of the magnetic field at these two points, we can gain a better understanding of how the Biot-Savart Law applies to different points in space. This can also help us visualize the direction and magnitude of the magnetic field at these points.

4. How does the Biot-Savart Law for finite wire differ from the Biot-Savart Law for an infinite wire?

The Biot-Savart Law for finite wire takes into account the varying angles and distances between the wire segments and the point of interest, while the Biot-Savart Law for an infinite wire assumes that the wire is infinitely long and straight. This assumption simplifies the calculation process, but it may not accurately represent the magnetic field behavior near the ends of a finite wire.

5. What are some real-life applications of the Biot-Savart Law for finite wire?

The Biot-Savart Law for finite wire has many applications in various fields, including electrical engineering, physics, and medical imaging. It is used to calculate the magnetic field produced by current-carrying wires in electronic circuits, to study the behavior of magnetic materials, and to guide the placement of electrodes in medical devices such as MRI machines. It is also used in the development of new technologies, such as magnetic levitation trains and particle accelerators.

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