Mutual Inductance between a coil and a long straight wire

In summary, the conversation discusses determining the EMF induced in a coil due to current in a wire and the importance of considering self inductance in the problem. The correct differential equation for this setup includes both mutual and self inductance and the current through the resistor is influenced by both. The solution to this equation does not match any of the provided options. The term I2*R can be viewed as the net EMF in the circuit.
  • #1
harsh22902
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2
Homework Statement
In the adjacent figure, the mutual inductance of the infinite straight wire and the
coil is M, while the self inductance of the coil is L. The current in infinite wire is
varying according to the relation I = at, where "a" is a constant and t is the time.
The time dependence of current in the coil is .
Relevant Equations
flux = L*i
flux due to a coupled coil = M* current through that coil
sss.jpg


In the given question they have not provided the dimensions of the coil so I assumed it to be very close to the wire and having negligible dimensions compared to the wire . Then EMF induced in the coil due to the current in the wire comes out as M*a . Which when divided by resistance gives option a . But the correct answer is option D. Also the initial change in flux is due to current in the wire so I did not consider self inductance.
 
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  • #2
You have to consider self inductance for this problem. There are two EMFs in this problem, one due to mutual inductance and one due to self inductance. We have to include both. The correct differential equation that describes this setup is $$M\frac{dI_1}{dt}+L\frac{dI_2}{dt}+I_2R=0$$ where ##I_2## is the current through resistor R, and we have included both EMFs (the EMF due to mutual inductance M ##M\frac{dI_1}{dt}## and the back EMF due to self inductance ##L\frac{dI_2}{dt}##).
)The solution to the above differential equation is indeed none of the options provided.
 
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  • #3
The current I2 in the equation , is it due to emf induced by mutual inductance?
 
  • #4
harsh22902 said:
The current I2 in the equation , is it due to emf induced by mutual inductance?
Well the mutual inductance is the primary cause if we can say that, but the self inductance also plays a role in its time dependence as that equation shows.
 
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  • #5
Also, the term I2*R that is actually the 'net' emf , right?
 
  • #6
Yes you can view it that way though it is actually the voltage drop in the resistance R but it is equal to the net emf as you say.
 
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  • #7
Understood it now, thank you !
 
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Related to Mutual Inductance between a coil and a long straight wire

1. What is mutual inductance between a coil and a long straight wire?

Mutual inductance refers to the phenomenon where a changing current in one circuit induces a voltage in another circuit. In this case, the coil and the long straight wire are the two circuits.

2. How does mutual inductance between a coil and a long straight wire affect the two circuits?

The mutual inductance between the coil and the long straight wire creates a magnetic field that links the two circuits. This results in an induced voltage in the coil, which can affect the current flow in both circuits.

3. What factors affect the mutual inductance between a coil and a long straight wire?

The mutual inductance between the coil and the long straight wire is affected by the number of turns in the coil, the distance between the two circuits, and the current flowing through the wire.

4. How is mutual inductance between a coil and a long straight wire calculated?

The mutual inductance between a coil and a long straight wire can be calculated using the formula M = μN1N2A/l, where μ is the permeability of the medium, N1 and N2 are the number of turns in the coil and the wire respectively, A is the area of the coil, and l is the distance between the two circuits.

5. What are some real-world applications of mutual inductance between a coil and a long straight wire?

Mutual inductance between a coil and a long straight wire is used in various electronic devices such as transformers, motors, and generators. It is also used in wireless power transfer systems, where the changing magnetic field induces a voltage in a receiving coil to transfer power without the need for physical contact.

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