# Exploding potato?

1. Jan 24, 2010

### theneedtoknow

I'm reading an electrodynamics textbook and in the preface there is a mention that the number of positive and negative charges in solid objects is extremely precisely balanced, and gives an example, that if there was an imbalance of even 1 part in 10^10, "a potato would explode violently".
How, exactly, would it explode?

2. Jan 24, 2010

### mgb_phys

Violently?

Presumably they mean that if the positive charge in the nucleas of an atom didn't exactly balance the negative charge on the electrons than the atoms would spilt apart.

3. Jan 24, 2010

### taylog1

Yes - each electron in the spud will be repulsed by every other electron, and attracted by every proton - with an excess of electrons there will be a net repulsive force, and the electrons are pushed apart (dragging their atoms with them, if we assume a potato is an insulator, and so the electrons are closely bound to the atoms).

4. Jan 24, 2010

### atyy

Last edited by a moderator: Apr 24, 2017
5. Jan 24, 2010

### Bob S

First, 1 gram of TNT = ~ 4000 Joules.

Let's make a capacitor with an inner radius a =.025 m, and outer radius b = 10 m, and put charge on it..

The capacitance is C = 4πε0ab/[b-a] ≈ 4πε0a for b>>a

If all the charge were on the surface of a sphere with inner radius a, the stored energy would be

W = Q2/2C = Q2/[8πε0a]

A 250 g potato will have about 140 mols of electrons = 96,000 x 140 Coulombs of electrons.

If the electron deficiency (proton excess) were 1 part in 1010, then

Q = 96,000 x 140 x 10-10 = 1.3 x 10-3 Coulombs.

So if all the charge were on the surface of a sphere of radius 0.05 m, the stored energy would be

W = Q2/2C = Q2/[8 πε0a] = 300,000 Joules, or ~ 75 grams of TNT.

If the charge were uniformly distributed throughout the potato, the stored energy would be even higher. Because the charge would be uniformly distributed throughout the potato, the explosion would be "violent".

Bob S

6. Jan 24, 2010

### DaveC426913

While fun to pretend what this would be like, let's not pretend this is happening in a contextual vacuum.

If there were an imbalance, the atoms would have never formed into a potato in the first place; they'd just be a pile of atoms, like dust, on the table (assuming that the table - and the planet it was situated on - were not similarly imbalanced).

So, what we're really talking about is a "what if the fundamental laws of physics could be changed at-will"-type question. Only with this ability could you get a potato in the first place.

7. Jan 24, 2010

### atyy

Nice! That answers my question. I made a similar calculation some time ago for a cell membrane and looking it up I see I got a 10-12 C difference which is 9 orders of magnitude less than what you got, so that checks out. https://www.physicsforums.com/showthread.php?p=1855399

In hindsight, I see I shouldn't even have needed to do the calculation, since we know that the membrane potential hardly changes the concentration of ions in the intracellular fluid, which is about 1023. So the charge difference should be about 1 part in 1020.

Last edited: Jan 24, 2010