The difference between Ampere's law & Biot-Savart Law

• PhiowPhi
In summary, the conversation discusses the concept of magnetic fields generated by infinite and finite wires at a certain point away from the wire. The person is struggling to understand why an infinite wire would generate a stronger magnetic field compared to a finite wire with the same dimensions and current applied. They question how all the current elements in the wire can contribute to the magnitude at the point in question and how the magnetic field is 3-dimensional. The use of Biot-Savart is suggested to calculate the full magnetic field.
PhiowPhi
When considering the magnitude of the magnetic field at a certain point (##P##) away from an infinite/finite wire, I can't understand how an infinite wire would generate a stronger magnetic field (##B##) in contrast to a finite wire that has the same dimensions and current applied, at the same point (##P##). I understand how to use the equations, yet I can't fully understand the concept.

Considering the case of an infinite wire:

At the point the magnetic field is point out of the page.
Case of the finite wire:

Where (A) is the current element region of focus.
Why are the different considering the same ##I## and dimensions for the two?
I found from other sources that all the current elements in the wire would contribute to the magnitude at point(##P##) but how is that so? If the magnetic field created by the current element loops around it:

If so, how can regions B,C contribute to point(##P##) for the two wires?

For the finite wire:

PhiowPhi said:
If the magnetic field created by the current element loops around it:
That is not the full magnetic field induced by the wire element. The full magnetic field is 3-dimensional, it just has its strongest region orthogonal to the wire.

You can use Biot-Savart to calculate that.

mfb said:
The full magnetic field is 3-dimensional, it just has its strongest region orthogonal to the wire.

For some reason I can't imagine that...

What is Ampere's law?

Ampere's law is a physical law that describes the relationship between the magnetic field around a closed loop and the electric current passing through that loop. It states that the line integral of the magnetic field over a closed loop is equal to the current passing through the loop multiplied by a constant known as the permeability of free space.

What is the Biot-Savart law?

The Biot-Savart law is a mathematical equation that describes the magnetic field produced by a steady current in a wire. It takes into account the distance from the wire, the direction of the current, and the strength of the current to calculate the magnetic field at a specific point in space.

What is the main difference between Ampere's law and Biot-Savart law?

The main difference between Ampere's law and Biot-Savart law is the type of current they describe. Ampere's law is used to calculate the magnetic field around a closed loop due to the current passing through that loop, while Biot-Savart law is used to calculate the magnetic field at a specific point in space due to a steady current in a wire.

When should I use Ampere's law versus Biot-Savart law?

Ampere's law is most useful when working with closed loops of current, such as a solenoid or a wire wrapped around a core. Biot-Savart law is more useful when calculating the magnetic field at a specific point in space due to a steady current, such as in a straight wire or a loop of wire.

Can Ampere's law and Biot-Savart law be used interchangeably?

No, Ampere's law and Biot-Savart law are not interchangeable. They are two different equations that describe different aspects of the relationship between electric currents and magnetic fields. While they may produce similar results in some cases, they cannot be used interchangeably in all situations.

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