# What's the difference between a positive and a negative current?

1. Say I have a wire, and I connect a current source on its left end, and a ground to its right end. Then using my power supply I source a positive current, does this mean that electrons will move from left to right or from right to left?

2. Also, what about joule heating? Is the direction of the temperature gradient created by the current change when I source a negative vs a positive current?

2. There should be no temperature gradient in either case because each point on the wire receives the same joule heating power. To see this, first we need to realize that the current will be uniform throughout the wire. Let's see why. If the current were to change at some point $p$, so that on the left the current is one amp, and on the right the current is two amps, then there would be more current flowing out of $p$ than flowing into $p$, so that charge would be building up at $p$. However, this build up of charge is physically unreasonable, so we conclude there must be no gradient of current at $p$, and so the current must be uniform everywhere. Assuming the wire resistance is also uniform, we find that the dissipated power $I^2 R$ is uniform everywhere and so the temperature should be uniform. (A small correction might be that the ends are cooler, but its not like one end would be cooler than the other end because the electrons have more potential there or something.)
• If the resistance in non-uniform, the current will still be uniform, so the area with higher resistance will have higher $I^2R$ power dissipated, and will be hotter. As you say, this does not depend on the direction of the current. Sep 25 '15 at 3:43
Given a particle of charge $q$ placed into an electric field, the equation of motion is $m \mathbf{\ddot{r}} = q\,\mathbf{E}(\mathbf{r},\mathbf{\dot{r}})$.
The direction of the electric field comes into play in the difference of potential $V_A - V_B$, according to whether your ground is at a lower or higher voltage (usually grounds are at lower voltages). Positive charged particles move in the direction where $V_A - V_B > 0$, negative charged particles do viceversa. Notice that the signe of the current is always the same, no matter whether the particles are positive or negative, because the possible minus signs in $j=qv$ cancel out. You cannot distinguish between positive particles moving from $A$ to $B$ or negative particles moving from $B$ to $A$. In general, though, electrons are the ones which move because positive carriers in materials are strongly bound.