Mutual inductance of a coil and straight wire

In summary: As for the mutual inductance, you can use the equation:Mutual inductance = flux(1)/i(2) = flux(2)/i(1)Where flux(1) is the flux through the loop due to the wire, and flux(2) is the flux through the wire due to the loop. You can use the expression you found for flux to calculate these values and then plug them into the equation to find the mutual inductance.
  • #1
Trogdor27
4
0

Homework Statement



A single rectangular loop is placed distance C from a wire of current I. The dimensions of the loop are BxA.

The loop and wire both lie in the same plane, and a is at right angles to I.

Derive an expression for the mutual inductance, given that you found flux in a previous question.

Homework Equations



B = mu I / 2R

Mutual inductance = flux(1)/i(2) = flux(2)/i(1)

The Attempt at a Solution



I have found the flux through the coil (I think it is right?):

flux = int(B.dA)

take the area as AxB, and let dA = b dr. The limits on the integral become c and c+a.

Integrate to find magnetic flux.

After finding flux, I am not sure how to go from here to the mutual inductance. I could just divide by i, but this seems WAY too simple for a question worth a lot of marks.

Or is it really just that simple?
 
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  • #2
Welcome to Physics Forums.
Trogdor27 said:

Homework Statement



A single rectangular loop is placed distance C from a wire of current I. The dimensions of the loop are BxA.

The loop and wire both lie in the same plane, and a is at right angles to I.

Derive an expression for the mutual inductance, given that you found flux in a previous question.


Homework Equations



B = mu I / 2R

Mutual inductance = flux(1)/i(2) = flux(2)/i(1)

The Attempt at a Solution



I have found the flux through the coil (I think it is right?):

flux = int(B.dA)

take the area as AxB, and let dA = b dr. The limits on the integral become c and c+a.

Integrate to find magnetic flux.

After finding flux, I am not sure how to go from here to the mutual inductance. I could just divide by i, but this seems WAY too simple for a question worth a lot of marks.

Or is it really just that simple?
Yes, that looks right.

By the way, don't forget the "π" in

B = μo I / (2π r)
 

Related to Mutual inductance of a coil and straight wire

1. What is mutual inductance?

Mutual inductance is a measure of the interaction between two electrical circuits or components. Specifically, it refers to the ability of a changing current in one circuit or component to induce a voltage in another circuit or component.

2. How is mutual inductance calculated?

Mutual inductance is calculated by taking the ratio of the induced voltage in one circuit or component to the rate of change of current in the other circuit or component. This is represented by the formula M = NΦ₂ / I₁, where M is the mutual inductance, N is the number of turns in the coil, Φ₂ is the magnetic flux through the coil, and I₁ is the current flowing in the straight wire.

3. What factors affect mutual inductance?

The most significant factor affecting mutual inductance is the distance between the two circuits or components. The closer they are, the stronger the mutual inductance will be. Additionally, the number of turns in the coil, the strength of the current, and the shape and orientation of the two circuits or components can also affect mutual inductance.

4. How does mutual inductance impact circuit performance?

Mutual inductance can have both positive and negative impacts on circuit performance. On the one hand, it can be used to create transformers and induce voltages in one circuit without direct electrical connection, which can be advantageous in certain applications. On the other hand, it can also cause unwanted crosstalk and interference in nearby circuits.

5. How can mutual inductance be minimized or controlled?

To minimize or control mutual inductance, the distance between the two circuits or components can be increased, and the orientation and shape of the circuits or components can be adjusted. Shielding materials can also be used to reduce the effects of mutual inductance. Additionally, proper circuit design and layout can help prevent unwanted interference from mutual inductance.

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