# Understanding energy conservation in a solenoid

• yosimba2000
In summary, the magnetic field generated by the solenoid can be increased by increasing the number of loops. The required energy to generate this field is proportional to the number of loops.
yosimba2000
So let's assume ideal wire, resistance = 0 Ohms. Also assume there is a magnetic ball 1 meter away and is attracted to the solenoid.

If you have a loop of wire and run a small current through it, you get a magnetic field. This field attracts the magnetic ball, over a distance of 1 meter.

If you have multiple loops and using the same current, you get an even stronger magnetic field. This field more strongly attracts the ball over a distance of 1 meter.

So hypothetically I can make 1 million loops, run the same current through it, and have something like ~1 million times stronger magnetic field.
With this strong magnetic field, I should be able to exert more magnetic force on the ball over the same 1 meter distance.
So without increasing the electrical energy input, I have increased by potential magnetic energy by ~1 million times (then it's transformed to kinetic as it attracts the ball), and this is all achieved by only adding additional loops to the solenoid.

How does this work? I understand there is no "conservation of force", but hypothetically it seems I should be able to use a very small energy input to get a very large energy output? I could use 0.000000001 Amps over a sall time and voltage, and given enough loops, I could move a 1 ton magnetic ball.

Last edited:
The energy required to build a magnetic field ##B(I,L)## that depends on the current ##I## and the self inductance of the solenoid ##L## is ##E=\frac{1}{2}LI^2##. This energy must be supplied by the voltage source that drives the solenoid. In your example we keep ##I=0.0000001A## constant but we increase the number of loops that is we increase ##L## hence we make the magnetic field stronger but we also make the required energy higher. We 'll draw more energy from the voltage source that drives the solenoid.

##L## for a solenoid is such that it increases according to ##n^2## (where ##n## the number of loops) while ##B(I,L)## increases linearly according to current ##I## and again linearly according to the number of loops ##n##. So ,while keeping the current constant, if you increase the numbers of loops, you increase the magnetic field linearly according to ##n##, but you increase L and hence the energy required by a quadratic factor ##n^2##.

yosimba2000, etotheipi, vanhees71 and 1 other person
yosimba2000 said:
How does this work? I understand there is no "conservation of force", but hypothetically it seems I should be able to use a very small energy input to get a very large energy output?
During the first period you generated a positive voltage that caused a positive current to begin flowing in the coil, to create the magnetic field. Positive current multiplied by positive voltage is real power input.

During the second period you dropped the voltage to zero and maintained the same current and field. Zero voltage multiplied by any current is zero power.

During the third period you present a negative voltage to the coil while the current and the field fall to zero. Positive current multiplied by negative voltage is real power recovery.

But you don't get it all back because there is an EM wave, continuing to radiate out to infinity.
The more magnetic field you generate, the more energy is radiated away into space.

What the others told you is correct. In addition, you equate force with energy. That's very wrong.

To avoid mistakes like that in the future, always make sure the units match. Force has units of Newtons. Electric power is measured in watts. Electric energy in watt seconds.

yosimba2000 said:
With this strong magnetic field, I should be able to exert more magnetic force on the ball over the same 1 meter distance.
So without increasing the electrical energy input, I have increased by potential magnetic energy by ~1 million times

anorlunda said:
What the others told you is correct. In addition, you equate force with energy. That's very wrong.

To avoid mistakes like that in the future, always make sure the units match. Force has units of Newtons. Electric power is measured in watts. Electric energy in watt seconds.

Ah sorry, I should have said the potential energy of the magnetic ball.

Thanks, I got it now :)

## 1. What is a solenoid?

A solenoid is an electrical device that consists of a coil of wire that creates a magnetic field when an electric current is passed through it. It is commonly used in electromechanical devices such as relays, door locks, and electric motors.

## 2. How does a solenoid conserve energy?

A solenoid conserves energy by converting electrical energy into magnetic energy. When an electric current flows through the coil, it creates a magnetic field, which can then be used to do work, such as moving a metal rod or attracting another magnet. This conversion of energy allows for efficient use of electricity.

## 3. What factors affect the energy conservation in a solenoid?

The energy conservation in a solenoid is affected by several factors, including the number of turns in the coil, the strength of the electric current, and the material of the core. A larger number of turns in the coil and a stronger electric current will result in a stronger magnetic field and therefore, more efficient energy conservation. Using a ferromagnetic core, such as iron, can also increase the strength of the magnetic field.

## 4. How can energy losses be minimized in a solenoid?

Energy losses in a solenoid can be minimized by using high-quality materials for the coil and core, as well as ensuring proper insulation to prevent leakage of the magnetic field. Additionally, using a low-resistance wire for the coil and minimizing the distance between the coil and the core can also help reduce energy losses.

## 5. What are the practical applications of understanding energy conservation in a solenoid?

Understanding energy conservation in a solenoid has many practical applications, including in the design and operation of various electromechanical devices, such as speakers, door locks, and MRI machines. It also plays a crucial role in the development of renewable energy technologies, such as generators and electric motors, which rely on efficient energy conversion in solenoids.

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