Ratio of Inductance between 2 Solenoids?

In summary, the ratio of the inductance of solenoid A to that of solenoid B is 2, taking into account the specified dimensions and the amount of wire used for each solenoid. However, the cross-sectional area of solenoid A may also be affected and cannot be accurately calculated without more information.
  • #1
David Day
12
1

Homework Statement


[/B]
1. Two solenoids, A and B, are wound using equal lengths of the same kind of wire. The length of the axis of each solenoid is large compared with its diameter. The axial length of A is twice as large as that of B, and A has twice as many turns as B. What is the ratio of the inductance of solenoid A to that of solenoid B?


2. Homework Equations

L = μ0N2A/L

where N is the number of windings, A is cross-sectional area, and L is the axial length.

The Attempt at a Solution


[/B]
I started by setting the inductance of solenoid B to LB = μ0N2A/L, and altering this equation for the dimensions of solenoid A as specified in the question such that

LA = μ0(2N)2A/2L = μ02N2A/L

in which case the ratio of A:B is 2.

However, I understand that because the question specifies that the same amount of wire is used for both solenoids, changing the length and winding number of solenoid A would also affect its cross-sectional area, but I'm not sure how it can be calculated.

If I calculated correctly, doubling the height of a cylinder but keeping volume constant would require the cross-sectional area to be decreased by half. In this case the inductance ratio of A:B would just be 1, but I don't think that's right.
 
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  • #2
David Day said:
However, I understand that because the question specifies that the same amount of wire is used for both solenoids, changing the length and winding number of solenoid A would also affect its cross-sectional area,
Yes.
but I'm not sure how it can be calculated.
Can you express the cross-sectional area in terms of the length of wire and the number of turns of wire?

If I calculated correctly, doubling the height of a cylinder but keeping volume constant would require the cross-sectional area to be decreased by half. In this case the inductance ratio of A:B would just be 1, but I don't think that's right.
There is no requirement that the volumes of the cylinders be the same.
 
  • #3
TSny said:
Yes.
Can you express the cross-sectional area in terms of the length of wire and the number of turns of wire?

There is no requirement that the volumes of the cylinders be the same.

Yeah, I was thinking that using the same amount of wire, the volume would be constant, which isn't actually the case.

So it seems to me that if the wire is of length x, and the circumference of the wire is 2πrN for each uniform winding, then x = 2πrN and r = x/2πN. I'm not sure if this is correct, though.
 
  • #4
David Day said:
x = 2πrN and r = x/2πN.
Looks right.
 
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Related to Ratio of Inductance between 2 Solenoids?

What is the ratio of inductance between two solenoids?

The ratio of inductance between two solenoids depends on their relative distances, number of turns, and cross-sectional areas. It can be calculated using the formula L2/L1 = (N2/N1)^2 * (r1/r2)^2, where L is inductance, N is the number of turns, and r is the distance between the solenoids.

How does the distance between the solenoids affect the ratio of inductance?

The ratio of inductance is inversely proportional to the square of the distance between the solenoids. This means that as the distance between the solenoids increases, the ratio of inductance decreases.

Does the number of turns in each solenoid affect the ratio of inductance?

Yes, the number of turns in each solenoid has a direct effect on the ratio of inductance. The more turns there are, the higher the inductance will be, resulting in a larger ratio of inductance between the two solenoids.

How does the cross-sectional area of the solenoids impact the ratio of inductance?

The cross-sectional area also has an effect on the ratio of inductance. A larger cross-sectional area means a larger amount of magnetic flux can pass through the solenoid, resulting in a higher inductance and a larger ratio of inductance between the two solenoids.

Can the ratio of inductance between two solenoids be greater than 1?

Yes, the ratio of inductance can be greater than 1. This occurs when the solenoids are arranged in a way that increases the magnetic flux linkage and results in a higher inductance in one solenoid compared to the other.

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