Magnetic field of an infinite wire

In summary, the conversation is about finding the magnetic field caused by an infinite wire using the Biot-Savart Law. The person has a question about the integration process and is seeking clarification on how to integrate the equation correctly. The response suggests using a standard substitution for the integral.
  • #1
asi123
258
0

Homework Statement



Hey guys.
So I've got a current which goes through an infinite wire and I need to find the magnetic field which is caused by the wire at point P.
I used the Biot–Savart Law and in the picture you can see what I came up with (sorry, no scanner today, I had to do it the short way :smile:).
So, my question is, how am I suppose to get from the green equation to the red one? I took the red equation from their answers.
Am I missing something?

Thanks.


Homework Equations





The Attempt at a Solution

 

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  • #2
You might want to recheck the Green equation, it seems that you did not integrate correctly.
 
  • #3
Hootenanny said:
You might want to recheck the Green equation, it seems that you did not integrate correctly.

Ops, my bag, how am I suppose to integrate it? :blushing:
 
  • #4
asi123 said:
Ops, my bag, how am I suppose to integrate it? :blushing:
No problem. That integral looks almost like a standard integral and can be evaluated using the same substitution as you would use for the standard integral... :wink:
 

1. What is the magnetic field of an infinite wire?

The magnetic field of an infinite wire is the region of space surrounding the wire where a magnetic force is exerted on charged particles. It is a vector field, meaning it has both magnitude and direction, and is typically represented by the symbol B.

2. How is the magnetic field of an infinite wire calculated?

The magnetic field of an infinite wire can be calculated using the Biot-Savart law, which states that the magnetic field at a point is directly proportional to the current flowing through the wire and inversely proportional to the distance from the wire. The equation is B = μ0I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire.

3. How does the direction of the magnetic field of an infinite wire depend on the current?

The direction of the magnetic field of an infinite wire is determined by the right-hand rule. If you point your thumb in the direction of the current, the curl of your fingers will give you the direction of the magnetic field. This means that the direction of the magnetic field will change if the direction of the current changes.

4. Does the strength of the magnetic field of an infinite wire vary along its length?

No, the strength of the magnetic field of an infinite wire does not vary along its length. This is because an infinite wire is assumed to have an infinite length, and therefore, the distance from the wire (r) in the Biot-Savart law equation will not change. However, the strength of the magnetic field will decrease as you move further away from the wire due to the inverse relationship with distance.

5. What are some real-world applications of the magnetic field of an infinite wire?

The magnetic field of an infinite wire has many real-world applications. It is used in electromagnets, electric motors, and generators. It is also important in the study of magnetism and its effects on charged particles. Additionally, understanding the magnetic field of an infinite wire is crucial in the design and construction of various electronic devices.

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