But how about a numerical value for the electric field between these conducting plates? If I just go straight down the middle from one plate to the other, I can get electric potential values for different y values. Here’s what that looks like:
Remember the relationship between the electric field and the potential. The electric field is the negative of the change in potential divided by the change in position. If you plot potential vs. position, this is the same as the slope. Notice that the plot above is a linear function. This means the slope, and thus the electric field, is constant. From the slope, I get a constant electric field of 0.713 volts per cm (0.00713 V/m). Oh, 1 V/m is the same as a newton per coulomb. Both are equivalent units for the electric field.
But wait! The electric field is related to the electric force, and that means it should be a vector. The value calculated above is from the slope, so it’s just a scalar value. Well, there’s an easy fix for that. Since I plotted the potential with respect to the y position, this gives me the y component of the electric field. To find the x component, I’d also need to plot electric potential in that direction.
But in this case, the potential really doesn’t change much in the x direction. This means the x component of the electric field would be zero V/m. Honestly, that’s the nice thing about these parallel conducting plates—they make a constant electric field in one direction.
Why Do We Need the Paper?
So, that’s a quick introduction to electric fields and electric potential difference. Now for an answer to an important question that you didn’t ask:
Suppose I take a 9-volt battery and use some wires to connect the terminals to two parallel strips of aluminum foil separated by a distance of 10 cm—without any paper. Could I repeat this experiment to calculate the electric field between these plates?
The answer is no. I mean, it should work. The theory is that you have a change in potential across the two pieces of aluminum and there is a change in distance. Since you have two parallel plates, the electric field should be fairly constant. But it won’t work. If you take your voltmeter and connect one probe to the negative strip and put the other one right in the middle, it should read 4.5 volts. Instead it will read zero volts.