Comparing Self-Inductance and Power Dissipation in Two Solenoids

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

Self inductance L of a solenoid = μN²S/l

N = Total number of turns
l = Length of the solenoid
S = Cross sectional area of the solenoid

From the language of the problem statement I am assuming that S and N of the two solenoids are same .This makes" l " different for the two solenoids .

Self inductance L will be different .

This means for equal currents magnetic potential energy will also be different .

Now since the two solenoids are of different lengths and diameter of the wires are also different , resistance of the two coils will also be different .This means for equal currents , power dissipated will also be different .

Since both L and R are different , then time constant will also be different .

So to me it looks like all the statements are correct i.e option 4)

Is that correct ?

 

[Orodruin]

From the language of the problem statement I am assuming that S and N of the two solenoids are same .This makes" l " different for the two solenoids .

That would not be how I read the problem. I read it as the solenoids being the same with the only difference being the wire thickness, i.e., replacing the wire but the new wire has exactly the same winding as the old. The thickness of the wire does not dictate the length of the solenoid.

 

[Jahnavi]

The thickness of the wire does not dictate the length of the solenoid.

If the number of turns are same and area of cross section is also same , length cannot be equal .

 

[Orodruin]

If the number of turns are same and area of cross section is also same , I think length cannot be equal .

Why not? There is no reason to assume that the length is $Nd$, where $d$ is the wire thickness.

 

[Jahnavi]

Why not? There is no reason to assume that the length is $Nd$, where $d$ is the wire thickness.

OK .

So , lengths of the two solenoids are same . In that case length of the wires will be different . Right ?

 

[Orodruin]

OK .

So , lengths of the two solenoids are same . In that case length of the wires will be different . Right ?

No, why? If the wires occupy exactly the same space, they will have the same length.

 

[Orodruin]

For example, look at this image from Hyperphysics:

If you draw the wire thinner, will the length of the wire be longer?

 

[Jahnavi]

If the wires occupy exactly the same space, they will have the same length.

But if wires occupy the same space , length of solenoids is same , length of wires is also same , then how can the area of cross section be same ?

 

[Orodruin]

I am sorry, I am not sure I understand the question. If the wires occupy the same space, obviously the cross-sectional area is also the same.

 

[Jahnavi]

I am sorry, I am not sure I understand the question.

No . In fact you are understanding the question . I am not

Looking at the figure you have posted , I am imagining things a bit differently. I am assuming a tightly wound solenoid with effectively no space between the adjacent loops .

 

[Orodruin]

I was referring to your question regarding the cross-sectional area in #8.

I am assuming a tightly wound solenoid with effectively no space between the adjacent loops .

That would violate the assumption that they have the same geometrical construction. That they have the same geometrical construction means that all spatial information is the same, length of solenoid, number of turns, cross-sectional area, etc.

 

[Jahnavi]

That would violate the assumption that they have the same geometrical construction. That they have the same geometrical construction means that all spatial information is the same, length of solenoid, number of turns, cross-sectional area, etc.

You are right

Do you agree option 1) should be correct ?

 

[Orodruin]

Yes.

 

[Jahnavi]

Thanks !