# Understanding energy conservation in a solenoid

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:

Homework Helper
Gold Member
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
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.

Staff Emeritus
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.

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

yosimba2000
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.

yosimba2000

Thanks, I got it now :)