Calculating the magnetic field of 3 piece wire

In summary, the conversation discusses a problem involving finding the magnetic field at a given point along a wire that forms a half-circle arc. The individual provides the values for the current and radius and uses the correct formula to solve for the magnetic field, which is found to be 1.14X10^-4T. The summary also verifies that the solution is correct.
  • #1
GrassPuppet
1
0
Okay I need some verification that I did this problem right. If not then please tell me where I went wrong.

Given a long wire going into the page with current also going in the same direction and then making a half-circle arc along the plane of the paper to the left, and finaly conituing to make a straight wire. Find the magnetic field at P which is at the center of the arc (center of circle if the arc were a full circle). I'm given the radius of the arc and the current.

i=5.78A
R=.0789m
I used phi=Pi
I attached the formula I used and a poor drawing of what the wire looks like.

segment.View attachment arc.doc

I got 1.14X10^-4T
 
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  • #2
Yes, your solution is correct. Your formula is also correct - the magnetic field at P is given by B = μ0*i/(2*π*R). Plugging in the values you provided, you get B = 4π*10^-7 * 5.78/(2*π*.0789) = 1.14X10^-4T. Therefore, your answer is correct.
 
  • #3


I cannot provide a response without seeing your calculations and the formula you used. However, I can guide you in the right direction. To calculate the magnetic field at point P, you will need to use the Biot-Savart Law, which states that the magnetic field at a point is directly proportional to the current in the wire and the distance from the point to the wire, and inversely proportional to the square of the distance.

First, you will need to break down the wire into smaller segments and calculate the magnetic field at point P due to each segment. Then, you can use the superposition principle to add up the individual magnetic fields to get the total magnetic field at point P.

To check if your calculations are correct, you can compare your result to the magnetic field formula for a circular loop, which is given by B = μ0I/2R, where μ0 is the permeability of free space, I is the current, and R is the radius of the loop.

I hope this helps and good luck with your calculations!
 

1. How do you calculate the magnetic field of a 3 piece wire?

The magnetic field of a 3 piece wire can be calculated using the formula B = μ₀I/2πr, where B is the magnetic field, μ₀ is the permeability constant, I is the current, and r is the distance from the wire.

2. What is the significance of the number 3 in the term "3 piece wire"?

The number 3 refers to the fact that the wire is made up of three separate pieces, each carrying a current in the same direction. This can affect the overall magnetic field produced by the wire.

3. How does the distance from the wire affect the magnetic field calculation?

The distance from the wire is a critical factor in the calculation of the magnetic field. As the distance increases, the magnetic field strength decreases, following the inverse square law. This means that the magnetic field will be weaker the farther away from the wire you are.

4. Can the magnetic field of a 3 piece wire be affected by external magnetic fields?

Yes, external magnetic fields can influence the overall magnetic field produced by a 3 piece wire. This is known as magnetic induction and is a key principle in electromagnetism.

5. Are there any limitations to using the formula for calculating the magnetic field of a 3 piece wire?

The formula for calculating the magnetic field of a 3 piece wire assumes that the wire is infinitely long and straight. In reality, most wires are not perfectly straight or have a finite length, so this can affect the accuracy of the calculation. Additionally, the formula does not account for any magnetic shielding or other external factors that may alter the magnetic field produced by the wire.

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