# Comparing Self-Inductance and Power Dissipation in Two Solenoids

• Jahnavi
In summary, the two solenoids have different lengths and cross-sectional areas, which means that the power dissipated will be different.
Jahnavi

## 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 ?

#### Attachments

• solenoid.jpg
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Jahnavi said:
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
Orodruin said:
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 .

Jahnavi said:
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.

Orodruin said:
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 ?

Jahnavi said:
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.

Jahnavi
For example, look at this image from Hyperphysics:

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

#### Attachments

• sol3.gif
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Jahnavi
Orodruin said:
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 ?

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.

Orodruin said:
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 .

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

Jahnavi said:
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
Orodruin said:
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 ?

Yes.

Thanks !

## 1. What is a solenoid?

A solenoid is a type of electromagnet that consists of a coil of wire wrapped around a metal core. When an electric current flows through the wire, it creates a magnetic field and produces a force that can move objects or control the flow of electricity.

## 2. How do you compare two solenoids?

To compare two solenoids, you can consider factors such as the number of turns in the coil, the size and shape of the core, the material of the wire, and the strength of the magnetic field produced. You can also compare their applications and performance in specific scenarios.

## 3. What is the purpose of comparing two solenoids?

Comparing two solenoids can help us understand the differences and similarities between them, and determine which one is more suitable for a specific application. It can also help us improve solenoid design and performance.

## 4. What are some common applications of solenoids?

Solenoids have a wide range of applications in various industries, including telecommunications, automotive, medical, and industrial. They are used in devices such as door locks, valves, relays, speakers, and electric motors.

## 5. How can the performance of a solenoid be improved?

The performance of a solenoid can be improved by using a larger number of turns in the coil, increasing the strength of the magnetic field, using a better quality core material, and reducing any resistance in the circuit. Additionally, optimizing the solenoid's design and placement can also improve its performance.

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