# Potential energy in Gauss' gun

## Homework Statement

For my extended essay as part of the IB, I am investigating the effect of changing the distance and the number of stationary ball bearings in a Gaussian gun.

I was hoping to look at the energy transfer during each stage of magnets and therefore calculate the efficiency. However, I am struggling to understand the equations for determining the potential energy.

I understand that magnetic potential energy U can be found using U=-mB where m is the magnetic moment and B the magnetic field but I'm not sure if this would be correct for this application as it relates to the orientation of the diopole in relation to the field.

I can't see how the ball bearing would have more potential energy in one orientation than the other as it is a soft magnet and therefore surely the regions of polarity would change? Could anyone help me with this? Thanks!

U=-mB

## The Attempt at a Solution

(Sorry it's all kind of in one part)

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berkeman
Mentor

## Homework Statement

For my extended essay as part of the IB, I am investigating the effect of changing the distance and the number of stationary ball bearings in a Gaussian gun.

I was hoping to look at the energy transfer during each stage of magnets and therefore calculate the efficiency. However, I am struggling to understand the equations for determining the potential energy.

I understand that magnetic potential energy U can be found using U=-mB where m is the magnetic moment and B the magnetic field but I'm not sure if this would be correct for this application as it relates to the orientation of the diopole in relation to the field.

I can't see how the ball bearing would have more potential energy in one orientation than the other as it is a soft magnet and therefore surely the regions of polarity would change? Could anyone help me with this? Thanks!

U=-mB

## The Attempt at a Solution

(Sorry it's all kind of in one part)

What do you mean about "orientation" of the steel ball bearing? And what do you mean about a dipole? Do you mean induced dipole from the gradient of the magnetic field leading into each coil stage?

What do you mean about "orientation" of the steel ball bearing? And what do you mean about a dipole? Do you mean induced dipole from the gradient of the magnetic field leading into each coil stage?

There's not that much I can find about it online but https://www.wired.com/2011/12/does-a-magnet-gun-conserve-momentum is quite useful.
Yes, I do mean coil gun but using short bar magnets rather than coils.

I think what I meant by the orientation was that the definition of magnetic potential energy from the equation U=-mB relates to the alignment of a dipole in the presence of a magnetic field and the energy required to rotate it - https://en.wikipedia.org/wiki/Magnetic_energy http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magpot.html .
What do you mean about "orientation" of the steel ball bearing? And what do you mean about a dipole? Do you mean induced dipole from the gradient of the magnetic field leading into each coil stage?
- yes I think that is what I mean
I think what I want is an equation that would give the potential energy a ball bearing would have as a result of being in the magnetic field in the same was as E = -GmM/r does for gravity.

Hope this makes some sort of sense! I'm only in year 12 in the UK so my knowledge of this area is really quite limited.

berkeman
Mentor
Yes, I do mean coil gun but using short bar magnets rather than coils.
I didn't know that bar magnets could be used with a coil gun. But I'm certainly no coil gun expert. You would need to constrain the path of the short bar magnet so that it can't rotate as it travels down the length of the coil gun, it would seem. Some sort of a plastic barrel maybe?
I think what I want is an equation that would give the potential energy a ball bearing would have as a result of being in the magnetic field in the same was as E = -GmM/r does for gravity.
I believe you can look at how magnetic solenoid actuators work (where energizing the coil pulls the metal shaft into the body of the coil. It is the gradient of the magnetic field that generates the force (at least when the ball bearing is not magnetized), AFAIK.

I didn't know that bar magnets could be used with a coil gun. But I'm certainly no coil gun expert. You would need to constrain the path of the short bar magnet so that it can't rotate as it travels down the length of the coil gun, it would seem. Some sort of a plastic barrel maybe?

I believe you can look at how magnetic solenoid actuators work (where energizing the coil pulls the metal shaft into the body of the coil. It is the gradient of the magnetic field that generates the force (at least when the ball bearing is not magnetized), AFAIK.

Thanks, I'll have a look at that. This is what I mean about how the gun works (sorry wasn't very clear)