# Energy and force in a solenoid with multiple wirings

• fogvajarash
In summary, a solenoid has length L = 2.0m, radius R = 28.0cm, field strength B = 2.7T. The field is maintained by superconducting wires, with cross section 2mm x 2mm, wound with a 2mm spacing between windings and 20 layers of winding. The current is I = 215A.
fogvajarash

## Homework Statement

A solenoid has length L = 2.0m, radius R = 28.0cm, field strength B = 2.7T. The field is maintained by superconducting wires, with cross section 2mm x 2mm, wound with a 2mm spacing between windings and 20 layers of winding. Use the result that the current is I = 215A.

a. If the coil were made of room-temperature copper (resistivity ρ = 1.680×10-8 Ωm), how much power would be consumed in maintaining this current?
b. The magnetic field strength falls, from its full value in the innermost layer of wires to zero in the outermost layer, so on average the wires feel half the field strength present inside the solenoid. Compute the force per unit area, pushing outward on the wires.
c. Find the ratio of the energy density stored in the field and the force per unit area acting on the wires.

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## The Attempt at a Solution

I have calculated the energy density stored, which should be 2.90x106J/m3. However, I can't seem to find the answer to a. I'm using the equation $R = \frac{pL}{A}$ and then $P = I^{2}R$. For the resistance, I'm taking the length to be $L = 2\pi r$ and the area to be the cross-sectional area of the wires. Then, the current is the result obtained. However, I'm not sure what's wrong with my reasoning.

On the other hand, for question b., I got that the force per unit area should be given by $F = \frac{BIl}{2A}$, where the length would be the length given by $L = 2\pi r$ and the area should be the product $A = 2\pi rw$, where w is one of the sides which is 2mm. However, this result as well is wrong. I really can't visualize how can multiple winding solenoids work. From this, then the result to c. should come easily.

Thank you for your time and patience.

Last edited:
L=2Pi.r sounds like the length of wire per single turn. How many turns in the total solenoid winding?

NascentOxygen said:
L=2Pi.r sounds like the length of wire per single turn. How many turns in the total solenoid winding?

It would be N = 1000 turns as we divide the total length by the spacing. I used this and i stilll get a wrong anser for a. (Using it as the total length of wire).

I don't make it 1000 turns.

NascentOxygen said:
I don't make it 1000 turns.
What do you mean? Is the result different?

fogvajarash said:
What do you mean? Is the result different?

Yes, I calculate a different number.

P = (I^2)(resistivity)l / A

A = 0.002^2
n = LW/0.002
l = 2pi*r*n

for a, that is what you should be using, I believe

## 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 passes through the wire, it creates a magnetic field that can be used to generate force or movement.

## 2. How does energy affect a solenoid with multiple wirings?

The amount of energy supplied to a solenoid with multiple wirings will determine the strength of the magnetic field it produces. The stronger the magnetic field, the greater the force and movement that can be achieved.

## 3. Can a solenoid with multiple wirings produce different forces?

Yes, the number of wirings in a solenoid can affect the strength of the magnetic field and therefore the force it can produce. More wirings will result in a stronger magnetic field and a greater force.

## 4. How do multiple wirings affect the efficiency of a solenoid?

Having multiple wirings in a solenoid can increase its efficiency as it allows for a stronger magnetic field to be generated with a lower amount of energy input. This can result in a more powerful and efficient solenoid.

## 5. Are there any limitations to using multiple wirings in a solenoid?

One limitation is that adding more wirings can increase the resistance in the circuit, which can result in a decrease in the efficiency of the solenoid. Additionally, the size and space constraints of the solenoid may also limit the number of wirings that can be used.

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