Mutual Inductance: Solving with Ampere's Law

In summary, the conversation discusses the use of Φ = M*I to find mutual inductance and the question of whether Ampere's law can be used in this situation or if Biot-Savart must be used instead. It is suggested to use a double integral to find the contribution of points on the first wire to the magnetic field at a general point on the second wire, and to integrate this over the length of the first wire to get the flux. The conversation also briefly touches on the B-field of a long straight wire.
  • #1
Frillth
80
0

Homework Statement



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Homework Equations



Φ = M*I
Biot-Savart law
Ampere's law

The Attempt at a Solution



I have the formula Φ = M*I, which means that to find the mutual inductance I simply need to find the magnetic flux through the top circuit due to the current in the bottom circuit. However, I don't yet have a solid grasp of Ampere's law. Is there a way to use Ampere's law in this situation, or am I going to have to grind it out with Biot-Savart?
 
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  • #2
Frillth said:
I have the formula Φ = M*I, which means that to find the mutual inductance I simply need to find the magnetic flux through the top circuit due to the current in the bottom circuit. However, I don't yet have a solid grasp of Ampere's law. Is there a way to use Ampere's law in this situation, or am I going to have to grind it out with Biot-Savart?

Looks like you will have a double integral for each point along the second wire for all the contribution from points on the first, then integrated over its own length.

See also:
http://en.wikipedia.org/wiki/Inductance#Mutual_inductance
 
  • #3
Can I use Biot-Savart to find the magnetic field at some general point (x,y) in the plane, then integrate that over the area of the top loop to get flux?
 
  • #4
What's the B-field of a long straight wire?
 

Related to Mutual Inductance: Solving with Ampere's Law

1. What is mutual inductance?

Mutual inductance is a phenomenon in which a changing magnetic field in one circuit induces a voltage in a nearby circuit. It occurs when there is a close physical proximity between the two circuits and there is a relative change in the magnetic field between them.

2. How is mutual inductance related to Ampere's Law?

Ampere's Law states that the magnetic field around a closed loop is proportional to the current passing through the loop. In the case of mutual inductance, the changing magnetic field in one circuit induces a current in the other circuit, which can be calculated using Ampere's Law.

3. How can mutual inductance be calculated?

Mutual inductance can be calculated using the formula M = N1Φ21/I1, where N1 is the number of turns in the first circuit, Φ21 is the magnetic flux through the second circuit, and I1 is the current in the first circuit. This formula is derived from Ampere's Law.

4. What are some applications of mutual inductance?

Mutual inductance has various applications, such as in transformers, where it is used to step up or step down the voltage in a circuit. It is also used in wireless charging, where a changing magnetic field is used to transfer energy between two circuits without the need for physical contact.

5. How does mutual inductance affect the behavior of circuits?

Mutual inductance can affect the behavior of circuits by inducing voltages and currents in nearby circuits, which can lead to interference and affect the overall functioning of the circuits. It is important to consider mutual inductance when designing circuits to prevent unwanted effects.

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