How Would an Imbalance of Charges Cause a Potato to Explode?

[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?

 

[mgb_phys]

How, exactly, would it explode?

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.

 

[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).

 

[atyy]

Really? Are the cell membranes not slightly charged? http://electrochem.cwru.edu/encycl/art-p01-plants.htm

 

[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

 

[DaveC426913]

if there was an imbalance of even 1 part in 10^10, "a potato would explode violently".
How, exactly, would it explode?

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.

 

[atyy]

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

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.