# Electric potential and conductors

• nuby
In summary, a single electric potential affects the atoms within a conductor, and the effect is dramatic depending on whether you apply a positive or negative potential.

#### nuby

Couple questions for you guys.

1. How does a single electric potential affect the atoms within a conductor. For example, if 100V is applied to a copper wire.. how do the copper atoms move/react to the voltage? (no current flowing)

2. Does positive or negative potential affect the wire differently? Or would it be the same effect?

Okay ... so you need a model in your head for what a wire really is. Here's one you can use if you don't already have one. A conductor is a crystal lattice with a sea of electrons floating around it. If the wire is neutral, no charge, there are just enough electrons in total to balance the positive nucleii of the crystal atoms. Most of the electrons are captive in the lattice, but some of the electrons in a conductor are free to move around, they are in the 'conduction band' from an energy standpoint. The slightest change in energy, or the slightest applied field, and they can move. (That's different than semiconductors.)

The wire itself is a long skinny potential well. Think of it like this: if an electron started to leave the wire, the wire would become more positive and it would be harder for the next electron to leave. This is actually going on all the time from thermal agitation: the electrons bounce around a lot and they start to bounce away from the surface of the conductor. They form a cloud around the conductor: their thermal energy is balanced by the surface field that builds because they've (partially) left the wire. The hotter the wire, the further they stray from the surface. When a wire gets really hot (like in a light bulb) they are straying pretty far and a small E field can coax them to leave. Look up the "Edison Effect" for details. It's the one major thing that Edison discovered and never capitalized on.

Shortest answer: the atoms don't hardly do anything (although if you make a WHOLE BUNCH of electrons move you can make the metal atoms migrate ... this happens in IC chips if you're not careful). Moving electrons also couples some energy to the atoms so they get hot, but if you have no current, there's very little of that.

Longer Answer: If you are applying the potential to one end of the wire and leaving the other to flap in the breeze, a detailed analysis would show that a wave propagates down the wire and bounces a bunch of times. It eventually settles down to a single potential. If you applied a positive potential, the cloud of electrons around the wire will be held more tightly and the cloud will shrink. If you applied a negative potential, the cloud would swell.

For the rest of this we need to put the wire in a vacuum. Since the electrons are in a cloud around the wire, we can get a current to flow by putting a terminal near, but not attached to the wire. The hotter the wire, the further we can place the second terminal to get the same current. There is an assymmetry here. Applying a negative potential to the wire makes the cloud grow, and the current increases. Applying a positive potential makes the cloud shrink and the current decreases. The effect is dramatic. Current flows easily in one direction, but almost stops in the other.

SO that's the long answer: the details of the distribution of charges around the wire change dramatically depending on whether you apply a positive of negative potential. The practical use of this effect led to vacuum tubes and the electronic revolution. So it is a big deal. Hope that wasn't too long.

## 1. What is electric potential?

Electric potential, also known as voltage, is a measure of the electric potential energy per unit charge. It is a scalar quantity that represents the ability of a charged object to do work on another charged object.

## 2. How is electric potential related to conductors?

Electric potential is related to conductors as it determines the flow of electric charge through a conductor. Conductors have a low resistance to the flow of electric charge and therefore, a lower potential difference is required for the charge to flow through them.

## 3. What is the difference between electric potential and electric field?

Electric potential is a scalar quantity that represents the potential energy per unit charge, while electric field is a vector quantity that represents the force per unit charge. Electric potential is dependent on the location and configuration of charges, while electric field is dependent on the presence of charged particles.

## 4. How is electric potential calculated for a conductor?

The electric potential for a conductor can be calculated by dividing the electric potential energy by the amount of charge on the conductor. This can also be represented by the ratio of the electric field to the distance from the surface of the conductor.

## 5. How does the shape of a conductor affect its electric potential?

The shape of a conductor can affect its electric potential as it determines the distribution of charges on the surface of the conductor. For example, a sharp point on a conductor will have a higher electric potential compared to a smooth surface, as the charge is concentrated at the point.