Mutual Inductance - Two rectangular loops

In summary, the conversation discusses two rectangular loops, an outer loop with length a and width b, and an inner loop with length c and width d. The problem states to apply a current to the outer loop and determine the expression for the mutual inductance between the loops. The solution involves using the equation V2 = M di1/dt and considering the superposition of each side of the outer loop. The final answer is given in terms of the original variables, a and b. It is important to note that the notation used should be carefully defined to avoid confusion.
  • #1
lukeb87
2
0

Homework Statement


Consider two rectangular loops. An outer and inner loop. Assign outer loop a length a and width b. Assign inner loop length c and width d.

Apply a current to the outer loop.

Determine an expression for the mutual inductance between the loops.


Homework Equations



V2 = M di1/dt
B(r) = (mu0*I) / 2*Pi*r
magnetic flux through loop = ((mu0*L*I)/(2*Pi)) * ln(b/a)
EMF = -d(flux)/dt


The Attempt at a Solution



Here is my attempt and a visual representation of the problem:

http://i910.photobucket.com/albums/ac301/lukebaldan/assign_attempt1.jpg" [Broken]

We know that mutual inductance can be determined via:

V2 = M di1/dt

My methodology is to rework the simple case consisting of a long infinite line and a rectangular loop. The solution is trivial (Double integral over area element involving the definition of the magnetic field outside of wire).

In this case we can consider the superposition of each side of the outer loop. The current is identical and the adjacent lines are at 90 degrees so we ignore them when considering the other side of the loop.

Therefore the contribution from the top and bottom lines is simply twice that of the simple single line case.

This is repeated for the sides.

Is my solution correct? I cannot think of another way to solve the problem. My attempt seems logical to me. Can anyone point me in the correct direction? Any help is much appreciated.

Thanks,
Luke
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
You should seriously clean up your notation! took me quite a bit of time to figure it out.

A and B are outer loop lengths. a and b are inner loop lengths (not c and d).

In your calculations, you have used variables a and b to define some other quantity even though a and b have already been used! Make sure you don't mess up because of that.

But other than that, the answer is right!

note that in the final answer

a = (B+'b')/2
b = (B-'b')/2
c = (A+'a')/2
d = (A-'a')/2

where 'a' and 'b' are the original variables as described in the problem.
 
  • #3
Hi there. Sorry i apologise. I meant to describe the problem in an easy fashion, My drawing is a much better representation of the problem.

Thanks for the acknowledgment.
 

1. What is mutual inductance?

Mutual inductance is a measure of the coupling between two electrical circuits, specifically the ability of one circuit to induce a voltage in the other circuit through changes in the magnetic field.

2. How is mutual inductance calculated?

Mutual inductance can be calculated using the formula M = k√(L1L2), where M is the mutual inductance, k is the coupling coefficient, and L1 and L2 are the inductances of the two circuits.

3. What factors affect mutual inductance?

The factors that affect mutual inductance include the distance between the two circuits, the orientation of the circuits, the size and shape of the circuits, and the electrical properties of the materials used.

4. How does mutual inductance impact circuit performance?

Mutual inductance can have both positive and negative impacts on circuit performance. It can be beneficial in certain applications, such as in transformers, where it allows for efficient transfer of energy between circuits. However, it can also cause unwanted interference and crosstalk in other circuits.

5. Can mutual inductance be controlled or adjusted?

Mutual inductance can be controlled to some extent by adjusting the factors that affect it, such as the distance and orientation of the circuits. It can also be minimized through the use of shielding and other techniques to reduce unwanted interference.

Similar threads

  • Electromagnetism
Replies
16
Views
932
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
5
Views
7K
  • Advanced Physics Homework Help
Replies
1
Views
4K
Replies
4
Views
3K
  • Advanced Physics Homework Help
Replies
1
Views
2K
Replies
6
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Advanced Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
651
Back
Top