Ampere's Law on Current Carrying Loop

In summary, both Ampere's law and the Biot-Savart law can be used to calculate the magnetic field density (B) around a current carrying wire. However, while Ampere's law is easier to use for a long straight wire, the Biot-Savart law is more suitable for a general situation, such as a current carrying ring. This is because the geometry of the situation affects the calculation of the line integral in Ampere's law, while the Biot-Savart law does not rely on this assumption.
  • #1
JustStudying
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I haven't seen anyone derive the magnetic field density (B) using ampere's law, only using Biot-Savart Law
any reason why?

if we cut the loop and loop at one end (of the new cut) and treat it as if it was a current carrying wire, then by ampere's law we'd get:

B = u*I / 2*pi*r

but however by the Biot-Savart Law we actually get

B = u*I / 2*r

anyone know why?
 
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  • #2
Ampere's law tells you that (line integral of B.dl along the loop) = μ0 * (flux of I through the loop). If you know from the geometry of the situation that B is constant along the loop, then calculating the line integral of B along the loop is easy. This is the case with a long straight wire. Here we draw a loop at a distance R from the wire. We know from symmetry that the value of B is everywhere constant along the loop, so the line integral of B along the loop is just 2*pi*R*B. In the case of a current carrying ring, no matter how you draw your Amperian loop, there is no way to draw it so that B is constant. So, while Ampere's law still holds, it is not very useful, since you don't know how to calculate the line integral. So you use the Biot-Savart law, which is more amenable to a general situation.
 

What is Ampere's Law on Current Carrying Loop?

Ampere's Law on Current Carrying Loop is a fundamental law in electromagnetism that explains the relationship between the magnetic field created by a closed loop of current and the current flowing through the loop.

How does Ampere's Law on Current Carrying Loop work?

Ampere's Law states that the magnetic field created by a current carrying loop is directly proportional to the current flowing through the loop and the number of turns in the loop, and is inversely proportional to the distance from the loop. This means that the magnetic field gets stronger as the current and number of turns increase, and weaker as the distance from the loop increases.

What is the significance of Ampere's Law on Current Carrying Loop?

Ampere's Law is important because it helps us understand and predict the behavior of magnetic fields created by current carrying loops. It also has many practical applications, such as in designing electromagnets and motors.

What are the limitations of Ampere's Law on Current Carrying Loop?

Ampere's Law is only applicable to steady currents. It also assumes that the current is evenly distributed throughout the loop and that the loop is a perfect circle. Additionally, it does not take into account the effects of external magnetic fields.

How is Ampere's Law on Current Carrying Loop related to other laws in electromagnetism?

Ampere's Law is closely related to other laws in electromagnetism, such as Faraday's Law of Induction and Gauss's Law. Together, these laws form the basis of Maxwell's equations, which describe the behavior of electric and magnetic fields.

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