Magnetic field due to current in straight wire(Biot-Savarts)

In summary: The magnetic field lines would still be perpendicular to the planes, but not necessarily to each other.Yes. The only nitpick is that a straight line doesn't define a plane. There are an infinite number of planes which contain the element. The magnetic field lines would still be perpendicular to the planes, but not necessarily to each other.
  • #1

san203

Gold Member
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Hello.
The Magnetic Field lines are concentric circles for a Straight wire.Hence the points above and below point B should not contribute to the magnetic field at A.
So Why do we integrate the expression across the whole length of the wire to get magnetic field at point A?
Magnetic.png
 
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  • #2
san203 said:
The Magnetic Field lines are concentric circles for a Straight wire.Hence the points above and below point B should not contribute to the magnetic field at A.

The "Hence" does not follow. The field at point A is the sum of contributions from all parts (infinitesimal segments of length ##dl##) of the wire. For an infinitely long wire (which is of course only an idealization) we integrate ##dl## from ##-\infty## to ##+\infty##. For a finitely long wire we integrate between some limits a and b.
 
  • #3
jtbell said:
The "Hence" does not follow. The field at point A is the sum of contributions from all parts (infinitesimal segments of length ##dl##) of the wire. For an infinitely long wire (which is of course only an idealization) we integrate ##dl## from ##-\infty## to ##+\infty##. For a finitely long wire we integrate between some limits a and b.

So you mean that every dl part of the wire contributes to the net field. But isn't the magnetic field lines Concentric? How can they intersect?
 
  • #4
What would the field look like around an infinitely short current segment [itex]dl[/itex]?

Would it still form concentric rings, or would it be different?
 
  • #5
The magnetic lines don't intersect.
 
  • #6
Remember that a magnetic field line is a line whose direction at every point is the direction of the RESULTANT field at that point. Just because the circle is centred at one point on the wire doesn't mean that that point is responsible by itself for the field line.
 
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  • #7
Philip Wood said:
Remember that a magnetic field line is a line whose direction at every point is the direction of the RESULTANT field at that point. Just because the circle is centred at one point on the wire doesn't mean that that point is responsible by itself for the field line.

I seemed to have overlooked that part. Maybe i am not thorough with the basics.
So, i guess a small circuit element is able to exert magnetic field at every point in its plane and that magnetic field is perpendicular the plane?
 
  • #8
Yes. The only nitpick is that a straight line doesn't define a plane. There are an infinite number of planes which contain the element.
 
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1. What is the Biot-Savart Law?

The Biot-Savart Law is a fundamental law in electromagnetism that describes the relationship between a steady electric current and the magnetic field it produces. It states that the magnetic field at a point in space is directly proportional to the current and the distance from the wire, and is also dependent on the orientation of the wire.

2. How do you calculate the magnetic field using the Biot-Savart Law?

To calculate the magnetic field at a point due to a current-carrying wire using the Biot-Savart Law, you need to know the current, the distance from the wire, the orientation of the wire, and the permeability of the medium through which the field is being measured. The formula for the magnetic field is 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.

3. What is the direction of the magnetic field produced by a current-carrying wire?

The direction of the magnetic field produced by a current-carrying wire can be determined by using the right-hand rule. If you point your thumb in the direction of the current, your fingers will curl in the direction of the magnetic field. Alternatively, the direction can also be determined by the orientation of the wire and the position of the point in relation to the wire.

4. How does the magnetic field vary with distance from the current-carrying wire?

The magnetic field produced by a current-carrying wire decreases as the distance from the wire increases. This relationship is inverse to the distance squared, meaning that the field strength decreases rapidly with increasing distance. This is because the magnetic field is spread out over a larger area as the distance increases, resulting in a weaker field at any given point.

5. What is the significance of the Biot-Savart Law in science and engineering?

The Biot-Savart Law is significant in science and engineering because it allows us to mathematically calculate and understand the magnetic field produced by a current-carrying wire. This is important in the design and analysis of electrical devices such as motors, generators, and transformers. It also plays a crucial role in the study of electromagnetism and the development of new technologies.

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