# Electric to kinetic energy

1. Sep 20, 2009

### Anden

1. The problem statement, all variables and given/known data

Ok, a few days back I gave a helping hand to a guy wondering about electric fields and how electrons act in them.
My thought for solving the question was U * q = 0,5mv^2, but as a clever person pointed out this makes no sense if the charge is negative. I've thought about it, and even looked it up in my physics book which uses the expression but does not bother to explain it.

2. Relevant equations

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3. The attempt at a solution

Well, if I knew I wouldn't be posting the question here.

But my theory so far is that if you use m * a = E * q, for a negative charge that would give a negative value for acceleration.
So to explain that I looked at the electric field lines, which always go from positive to negative.
So if you use an electron it would make sense that the acceleration would be negative since it accelerates in the opposite direction of the electric field.

So if I then put a negative sign in front of the electric field value, the acceleration would measure as positive in the opposite direction, that is acceleration would be negative for positive charges. To me that makes sense because if you "sit" at the positive pole, the electric field will "flow" away from you, while it would "flow" towards you if you were at the negative pole.

The expression can be rewritten into q * E * d = 0,5mv^2

My questions then is: Following the reasoning I provided, can I put a minus sign in front of the electric field value? Is my reasoning sound, or have I completely misunderstood everything ?

I'm happy for any help I can get

2. Sep 20, 2009

### RoyalCat

Energy is a scalar quantity, as is potential difference, trying to use vector quantities to describe it will just confuse you. I know it confuses me. ^^;

I think we should go back to the definition of what a potential difference is. It's like a height difference, with respect to gravitational potential energy.

If I put a charge in between a potential difference $$U_{AB}$$, then if I let it travel from point A to point B, then the work done on it will be $$U\cdot q$$

What is this work equal to? (Hint, it's not just the total kinetic energy, think difference, and remember that potential differences can be negative)

The direction of the field is defined as the direction of the force a positive charge would feel if placed at that spot. The direction of the force (±) is determined by the sign of the charge, the field always remains positive, as it was defined.

Last edited: Sep 20, 2009
3. Sep 20, 2009

### Anden

Ok, I'm trying to understand this, I've tried to get some conclusions out of it, please tell me if they're right or wrong.

The energy from point A to point B is not equal to the total kinetic energy, but to the change in kinetic energy?

If I use you height analogy, if the electrons are at the negative pole, they would be on a "cliff", thus when they travel to the positive pole this will lead to a negative change in potential energy, is that correct (The Electrons "fall" down)?

If it's correct, then I think I get why the expression above makes no sense ;)

I think some of the things you're saying is a difference in schooling, I was always taught to define my own "zero-line". That way one can create their own closed system, in which the total kinetic energy is equal to the change in potential energy.
For example in your case it's change in kinetic energy, because almost all electrons have kinetic energy already, am I correct?

4. Sep 20, 2009

### RoyalCat

Well, to be more precise, the electrons would fall up! Since it is the positive charges that accelerate when traveling from a higher potential to a lower one.

5. Sep 20, 2009

### Anden

Got it ;), thanks for your help!