Electric charge is the stuff electricity is made of; thus, when we “charge a battery,” we build up more electric charge at its terminals. There is a simple formula that describes the flow of these tiny particles responsible for electric current, and here it is:
J = v × n × e
Figure 21.5 If a particle moves at an angle to the direction of flow, we can “break up” its velocity into “forward” and “sideways” velocities. The arrow-lengths are proportional to the velocities they represent. The forward velocity is always less than the total velocity because part of the total goes toward sideways motion.
But only the forward part of the motion can contribute to the current; sideways motion doesn’t count, and backward motion would actually reduce the flow. So, for each particle, we should pick out and include only the component of its motion that is along the direction of the flow; if the motion is at an angle, we simply break down the velocity (as shown graphically in ) into a sideways velocity (vs) and a forward velocity (vf) along the direction of the flow. Backward velocity will be (–vf), the negative sign indicating that the particle is moving oppositely. But there is one more thing: Since the particles could all be moving in different directions, to obtain the net flow, we will need to take the average of the forward component of the velocities of all the particles. In physics, an average of a quantity is often indicated by placing a “bar” or horizontal line over its symbol, in this case, v. The upshot of all this is that we simply replace the velocity factor (v) in our original formula with the average of the velocity components in the direction of the flow, so our final formula for the current reads:
The quantum view is somewhat more sophisticated, but the end result is quite the same.