# Two nested solenoids and their magnetic fields

• MahalMuh
In summary, for b) the solution involves using Faraday's law to calculate the generated emf as a function of time, with the necessary components already provided. It may also be possible to utilize the constant value of B1 in this calculation.
MahalMuh
Homework Statement
We have 2 solenoids. The smaller (2) is inside the large one (1) with the axes aligned. Length1 is 0.63, radius1 0.051 m and N1 670 turns. The smaller length2 0.23 m, radius2 0.031 m and N2 260 turns. The larger solenoid has sine form AC with amplitude of I1 1.51 A and frequency1 120 1/s.

a) What is the biggest magnetic field B1 of the larger solenoid?
b) How large is the highest voltage V2 of the smaller solenoid?
Relevant Equations
B1 = u0*N1*I1 / length1
Several forms for M, inductance
I = I0 * sin(frequency*t)
Faradays's law for V =
a) is pretty clear and got correct but b) I'm struggling with.

For b) I guess one could take the derivative of I and specify the moment t when you can plug that into Faraday's law. Or could this be solved somehow with inductance?

Hi,

You didn't write down Faraday's law, but that is indeed what you need.

Faraday's law needs ##\displaystyle{d(BA)\over dt}## and you have all you need to calculate the generated emf, which then comes out as a function of time.

(I am fairly certain you are allowed to use B1 as if it's constant over the length of the small coil).

## 1. What is a solenoid?

A solenoid is a coil of wire that carries an electric current and produces a magnetic field. It is often used in electronic devices and electromechanical systems.

## 2. How are two nested solenoids different from a single solenoid?

Two nested solenoids consist of two coils of wire wrapped around each other, whereas a single solenoid only has one coil. This results in a stronger and more concentrated magnetic field in the center of the nested solenoids.

## 3. What is the purpose of using nested solenoids?

Nested solenoids are used to create a stronger and more uniform magnetic field compared to a single solenoid. This is useful in applications such as particle accelerators, MRI machines, and speakers.

## 4. How does the direction of the current affect the magnetic field in nested solenoids?

The direction of the current in each solenoid affects the direction of the magnetic field. When the currents in both solenoids are in the same direction, the magnetic fields add together and become stronger. When the currents are in opposite directions, the magnetic fields cancel each other out.

## 5. Can the strength of the magnetic field in nested solenoids be adjusted?

Yes, the strength of the magnetic field in nested solenoids can be adjusted by changing the number of turns in the coils, the current flowing through the coils, or the distance between the coils. These factors affect the magnetic field strength according to the solenoid's formula: B = μ0nI, where B is the magnetic field strength, μ0 is the permeability of free space, n is the number of turns, and I is the current.

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