# B Voltage applied to urchin-like iron spheres in salt water?

#### Misha Kuznetsov

Hello, if I had salt water and put microscopic spheres with iron spikes in (a lot of them, say 1,000). Then if a high static charge was applied to the water (say 500,000 volts), what would happen? My intuition tells me that the electric field would concentrate on the tips of the spikes, making all of the spheres repel one another.

I'm picturing spheres that look something like this.

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#### Cutter Ketch

hmmm. Well first you can't apply 500,000 V of static charge to the water. Current will flow to neutralize the charge. That's ok. Instead we'll say there are plates above and below the water but not in contact with the water with 500,000V. Next, the voltage is les important than the field strength. How big of a gap (i. e. how much water are we putting that potential across?). So instead of 500,000 V of potential, let's say we have 500,000 V / m of field strength. The first thing that will happen is the water will polarize. Charge in the water will migrate to cancel the field. Perhaps instead of salt water we should deionize the water so there is very little free charge. Anyhow let's say we charge the plates all we need to to create the desired field strength inside the water. There is a limit to the field strength that can be supported in water. At a high enough field the molecules actually get pulled apart. Fortunately that happens at a few GV/m so we are ok there. Now you put in the spiked balls. You say the spikes are iron. Can I assume the whole ball and spikes are iron? They won't acquire any net charge. What they will do is polarize. The charge will move in the electric field negative one way and positive the other. You are correct the field will concentrate in the tips of the spikes. This will be a problem if the field strength exceeds the breakdown field strength of the water. Well, let's say it doesn't. Although the field is very strong close to the points of the spikes at a distance

#### Cutter Ketch

Oops accidentally hit post. As I was saying at a distance large compared to the sharp points, the points don't matter so much and you'll get the same effect as if they were smooth balls. Now you have a solution of balls that are polarized by the external field. Now we get to your original question. The polarized balls won't want to be next to each other transverse to the field, so you may have the right idea that they would spread out that way. On the other hand they would line up along the field attracted into chains. They are conductive, so I think the charge would transfer eventually leaving a layer of positively charged spheres at the top of the layer of water and a negatively charged layer at the bottom. And yes I thing the spheres in the two layers would repel.

#### Misha Kuznetsov

Interesting answer, but I was picturing a Van de Graaff generator, that would charge up the salt water, adding extra electrons to it (so that the charge wouldn't be neutralized). Would the electrons just disperse evenly in the water or would they concentrate on the spheres due to their sharp needles?

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#### Misha Kuznetsov

I just thought of something: since electronegativity of oxygen is higher than iron, would the charges not go into the iron spheres at all?

#### Cutter Ketch

Ahh. Ok. So the water is "floating" (insulated or isolated so that it can hold this large potential to ground). The charges distributes themselves according to their mutual repulsion to get as far away from each other as possible. This means they go to the outer surfaces of the water or whatever structure holds the water. They distribute so that the internal electric field is zero (because if it weren't, the charges would move in the field until it was) and the potential everywhere within the floating structure, water included is the same. There is no internal field, and I nternally there is no difference to having no charge. Nothing happens to the spheres.

"Voltage applied to urchin-like iron spheres in salt water?"

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