# Electric field in a capacitor

The textbook talks of large parallel plate capacitors in which the electric field is uniform in the space between the plates and is zero outside. In finite capacitor, fringing of field makes the field look different near the ends. In this experiment you study the potential variation in and around the capacitor.

## Procedure

You need a plastic box with two aluminium plates which can be held at a distance and parallel to each other, a battery or power supply, multimeter, graph paper etc.

Place the plates in the box and fill the box with water up to about half the height. Connect the battery to the plates through a switch. Connect the common of multimeter to the plate connected to negative terminal of the battery. Make the multimeter mode DC Voltage. Now wherever you put the other probe of the multimeter, you will get the potential of that point with respect to the negative plate of the capacitor.

Measure the potential perpendicular to the plates in three regions (a) near the middle, (b) near 1/4 of the length of a plate, and (c) at the edge. Each time measure it at a regular interval of say 5 mm and present the data on distance from the negative plate and the potential there.

Measure the potential parallel to the plates in three regions (a) near the middle, (b) near 1/4 of the distance between the plates, and (c) close to a plate. Each time measure it at a regular interval of say 5 mm and present the data on distance from the negative plate and the potential there.

Make more observations close to the plates as there could be sharper variation.

Draw graphs for these variations.

1. Is the electric field components perpendicular to the plates constant everywhere in the capacitor?
2. Is the electric field components parallel to the plates zero everywhere in the capacitor?

## Variant

We study in electrostatics that if we move in the direction of the electric field, the electric potential decreases. This demonstration is a useful way to understand it as we can see the change of potential in the multimeter. There is no need to visualize it in our minds.

You need two aluminium plates, a glass/plastic trough, water, a battery, a multimeter and some connecting wires and a little plasticine.

1. Fix the two aluminium plates in plasticine and put it on the two edges of the glass/plastic trough. Pour water into the trough.
2. Connect the two plates with the two terminals of the 9 V battery. Connect the left plate to the positive terminal of the battery and the right plate to the negative terminal.
3. Now connect the black lead (common terminal) of the multimeter to the aluminium plate on the right.
4. Move the other terminal (red lead) of the multimeter from left to right. Note the voltage in the multimeter. It decreases as we move towards right. Why?
5. Now move the multimeter lead parallel to the plates. Do you see any change in voltage of the multimeter. Why?

The left aluminium plate is connected to the positive terminal of the battery so the direction of electric field is from left to right. But as we move in the direction of the electric field the potential decreases. So the multimeter shows a decrease in the voltage which is the potential at that point with respect to the potential of the common terminal.

When we move parallel to the plates there is no change in potential because we are moving on an equipotential surface.

Point of discussion: The presence of water in the trough is mandatory for the multimeter to show any voltage. Water being a conductor (a poor one though with dielectric constant = 80) allows the current to flow through the multimeter enabling it to show the voltage.

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