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# 3.2: Activities

## Things You Will Need

All you will need for this lab is the Java-based PhET simulator described in the Background Material. Go ahead and run this simulator now for use in the activities below.

## Parallel-Plate Capacitors

Click on the "Introduction" tab at the top of the simulator window to reveal a system consisting of a battery, two wires, and a parallel-plate capacitor.

1. Confirmations – There are many meters that can be selected in the right border. We will start by confirming that they provide values that are consistent with relations we have seen before.

Set the voltage of the battery to its maximum ($$1.5V$$), the plate area of the capacitor to the maximum value ($$400.0mm^2$$), and the separation to the minimum value ($$5.0mm$$).

1. Check the box for the capacitance meter. Perform a calculation using other values given to show that the value on this meter is consistent with those other values. How does this value change when the voltage supplied by the battery is changed? Does this make sense?
2. Check the box for the plate charge meter. Perform a calculation using other values given or previously-calculated to show that the value on this meter is consistent with those other values. How does this value change when the voltage supplied by the battery is changed? Does this make sense?
3. Check the box for the stored energy meter. Perform a calculation using other values given or previously-calculated to show that the value on this meter is consistent with those other values. How does this value change when the voltage supplied by the battery is changed? Does this make sense?
4. Disconnect the battery, and a slider for the plate charge appears. Set the amount of charge to the maximum ("lots (+)"). Use the values given by any two of the three meters on your screen to compute the potential difference between the plates (you will need to zoom-out the stored energy meter to see the value). Check the box for the voltmeter and use it to confirm your calculation.
5. Check the box for the electric field detector (you may need to zoom-out to see the value). This simulator assumes (as we usually do) that the field between the plates is uniform, and ignores "fringe effects" near the edges of the conductors. That is, the field is assumed to be zero outside the confines of the box defined by the two plates (you can confirm this by moving the probe). Confirm the electric field strength between the plates in the following two ways:
• Using the reading on the voltmeter.
• Using the reading on the plate charge meter.
1. Energy – Next we explore more deeply the nuances of the energy stored in the field of this capacitor.

Close all of the meters except for the stored energy meter and the electric field detector, leave the battery disconnected, and the plate charge at the maximum setting.

1. Confirm that the stored energy meter reads the correct value using the reading on the electric field detector. [You may not use (or recalculate) values for the plate charge, voltage difference, or capacitance for this calculation.]
2. Predict what will happen to the electric field strength if the plate separation is increased to its maximum ($$10.0mm$$). Based on this prediction, further predict how the stored energy will change when the plate separation is increased in this way. Test your predictions by dragging the plates apart using the vertical green arrows.
• Explain what happens in terms of the energy stored in the electric field.
• Explain what happens in terms of work performed on the system, and compute the constant attractive force between the two plates during the process.
3. Predict what will happen to the electric field strength if the plate area is decreased to its minimum ($$100.0mm^2$$). Based on this prediction, further predict how the stored energy will change when the plate area is decreased in this way. Test your predictions by dragging the plates to the smaller area using the diagonal green arrows.
• Explain this in terms of the energy stored in the electric field.
• Explain how external work is performed on the system in this case.

Return the plate area to its maximum, and the separation to its minimum, and click the "Connect Battery" button, making sure that the voltage of the battery is at its maximum value of $$1.5V$$. It's not hard to guess what will happen when we expand the separation to twice its current value. The voltage difference between the two plates is held fixed by the battery, and since $$\Delta V = Ed$$, and $$d$$ is doubled, the electric field has to get weaker by a factor of 2. Halving the electric field reduces the energy density $$u=\frac{1}{2}\epsilon_oE^2$$ by a factor of 4. The volume is doubled, so the total energy stored (the product of the energy density and the volume) in the field goes down by a factor of 2. But we must add work to the system to pull these oppositely-charged plates apart, so if we are adding energy to the system and the energy stored in the capacitor is going down, what has happened to the missing energy?

1. Account for this apparent discrepancy in the energy accounting.
• Confirm with the simulator using the stored energy meter that the energy in the capacitor does indeed drop to half its original value when the separation of the plates is doubled.
• When you expanded the plates, the simulator provided some transient animation (which you can repeat over and over if you need to), which should give a hint about where the energy went. Explain.

## Dielectrics in Capacitors

Click on the "Dielectric" tab at the top of the simulator window to reveal a system consisting of a battery, two wires, a parallel-plate capacitor, and a yellow cube of dielectric material. Disconnect the battery, dial up the plate charge to the maximum, and leave the dielectric constant at 5.00 (set on the slider in the right panel). This simulator is useful for exploring many aspects of dielectrics in capacitors (whether they are connected or disconnected from the battery), including the strength of the polarization field, the strength of the total electric field, the effect of the dielectric on the capacitance, and so on. You are encouraged to do this exploring, and perhaps playing with this will be useful for helping with conceptual understanding on assigned homework problems. But for this activity, we will "experimentally" examine the force exerted on the dielectric as it moves between the plates (see the discussion in the text reference on this subject given in Background Material for more details of this phenomenon).

1. Keeping in mind that the potential energy gets smaller as an object moves in the direction of the conservative force exerted on it (think of a stone falling under the influence of gravity), determine the direction of the force on the dielectric block by sliding it back-and-forth within the capacitor plates. You may use any meters you feel will be helpful.

Connect the battery and repeat the procedure above.

1. At any given position for the dielectric, it "doesn't know" that the battery is connected (indeed, we could charge the plates with the battery and then disconnect it, leaving the charge on the plates), and since it is the charge that ultimately exerts the force on the dielectric's polarization charge, this means that for a given charge on the plates, the force on the dielectric should be the same whether the battery is connected or not. Is this result reflected in the potential energy change? Once again, observing the transient animation of the simulator when moving the block with the battery connected provides a clue.

## Multiple Capacitors

Click on the "Multiple Capacitors" tab at the top of the simulator window to reveal a system consisting of a battery, two wires, and a parallel-plate capacitor. Set the voltage of the battery to its maximum ($$1.5V$$), and the capacitance of the parallel plates to a value of ($$1.20\times 10^{-13}F$$).

1. From the starting values given above, compute the amount of charge that comes off the positive terminal of the battery to the top plate of the capacitor. Confirm this value with the appropriate meter.
2. Check the circle for "2 in series" in the right panel. Your task is to set the two capacitances such that $$C_1=\frac{3}{4}C_2$$, and the same amount of charge comes out of the battery. You must not do this by trial and error! Show how you solve for these capacitances, then verify the resulting calculation with the simulator.
3. Check the circle for "2 in parallel + 1 in series" in the right panel. This time you are given that the three capacitances are equal ($$C_1=C_2=C_3$$), and once again you need to determine what these capacitances need to be for the same amount of charge to come out of the positive terminal of the battery. As before, perform the calculation first, then verify the result in the simulator.

## Lab Report

Download, print, and complete this document, then upload your lab report to Canvas. [If you don't have a printer, then two other options are to edit the pdf directly on a computer, or create a facsimile of the lab report format by hand.]