ELECTRIC FORCE MEASURED WITH A BALANCE SUMMARY

ELECTRIC FORCE MEASURED WITH A BALANCE SUMMARY

PHY109 Lab 1 Electric Force Balance

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ELECTRIC FORCE MEASURED WITH A BALANCE SUMMARY

When a voltage difference is applied to two parallel metal plates electric charge builds up on each of them. The opposite charge on each plate causes an electrostatic attraction between them. A mirror and a laser beam are used to precisely judge the disturbance of the plates due to the attractive force. By turning off the voltage and reproducing the disturbance by adding mass to the top plate,

the magnitude of the electric force and therefore permittivity constant o can be determined.

THEORY

If a positive charge Q is placed on large flat plate, as shown in Figure 1, the magnitude of the electric field near the plate is

1

02

Q E

A 

where A is the area of the plate. The constant o is the permittivity constant (also called vacuum dielectric constant),

120 28.85 10 Newton

Volt    .

In this lab we will use a simple force balance to calculate a reasonable

estimate of o. If a second charge –Q is placed on a second nearby parallel plate, the magnitude of the force between the plates is

2

1

02   

Q F QE

A

The charges are placed on the plates by a voltage source. The total electric field between the two

plates is twice 1E because the fields from the two charges add together. The voltage is

𝑉 = 2𝐸1𝑦 = 𝑄𝑦

𝜀0𝐴

where y is the distance between the plates. Combining these equations gives 2

0

22 

AV F

y

 .

Alternatively, the same deflection could be achieved by putting a small mass on the plate, so F = mg. By finding the mass that corresponds to the same deflection one can know the force, and

hence determine the permittivity constant o.

REFERENCE

Cutnell and Johnson chapter 18.

Figure 1. Two flat plates of area A separated by a distance y.

y

+Q

-Q

PHY109 Lab 1 Electric Force Balance

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SAFETY 1) While the experiment equipment is designed with safety high voltage is involved in this experiment. Always be careful, read the lab carefully and follow the instructions closely. If anything goes wrong turn off the power and ask your TA for help. 2) Turn off the power before you touch the apparatus, and never increase the voltage above 300 Volts. 3) Don’t look directly at the laser beam. Shine it on your hand to see if it is working. 4) Be gentle with this system. It is easily damaged.

EQUIPMENT AND PROCEDURE

The balance, shown in Figure 3 and sketched in Figure 2, has one fixed plate and a second plate which rides on a knife edge and thus can be rotated towards the first by the electrostatic force. A mirror rides on the frame of the moveable rod. A laser bounced off the mirror is used to detect its deflection. The counterweight is used to adjust the distance between the plates. Damping of the mechanical vibrations is provided by a paddle extending down from the frame and passing between two magnets.

1. ADJUST THE BALANCE Make sure the two plates are parallel and the top plate wobbles up and down slightly when you touch it gently. If necessary adjust the position of the counterweight behind the mirror until the moveable plate sits about 2-3 mm above the fixed plate.

1.1. INITIAL MEASUREMENTS Using a ruler measure and record the following in your Excel file:

1) The distance between the two plates (y) 2) The distance between the center of the plates and the axis of the pivot (X, shown in Figure 2) 3) The area of each square plate (measure the length of a side and use A = L2).

mirror

counter weight

magnetic damping

knife edge

voltage connector for fixed plate

voltage connector for moving plate

plates

X

ruler

Rod lifter knob

laser

Figure 2. A force is generated between the two green plates by applying opposite voltages or by placing masses on the plates.

If the top plate doesn’t move with gentle touches, lift the frame with the moveable rod carefully by turning the knurled “rod lifter” knob. If necessary, clean the knife edges. Adjust the leveling screws on the base of the apparatus so that it sits firmly on the table

If the top plate isn’t parallel to the bottom one, loosen the screws on the fixed plate, and twist it to make it parallel. Tighten all the screws.

Figure 3. Picture of apparatus

with power supply attached.

Power supply should be off for the

first part.

PHY109 Lab 1 Electric Force Balance

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1.2. CHECK THAT VOLTAGE CAUSES DEFLECTION To avoid electrocuting yourself or your partner: NEVER TOUCH THE APPARATUS WHILE THE VOLTAGE IS ON. Set the voltage to zero before turning on the power source. Read the voltage on the voltmeter, (shown in Figure 4). Make sure the AC/DC switch is set to “DC” and the center knob is set to “1000 V”. Very slowly increase the voltage. You should notice that the electrostatic attraction between the two plates moves the laser spot on the meter stick.

Your goal is to adjust the voltage until the distance between the plates is about one half of what it was before you turned the power on.

If the laser spot doesn’t move: don’t increase the voltage above 300 V. The spacing y is probably too large. Turn off the power supply, adjust the counter weight to decrease y, then turn on the supply to check that it will move.

If the plates stick together: y is too small. Turn off the power supply, adjust the counterweight to increase y, then turn on the supply to check that it will move.

Once you have verified your setup works, turn off the power supply. Measure again the distance between the plates, y, to ensure they return to their original positions.

2. MEASURING THE DEFLECTION WITH THE LASER Purpose: to use the deflection of the laser beam to accurately measure the distance y between the plates, necessary to calculate the electrostatic force.

With the power supply off: Turn on the laser, and verify that the beam reflects off the mirror and hits the meter stick. Adjust the position of the laser if necessary. Measure and record in Excel the distance from the mirror to the ruler, D. Measure and the height of the laser on the ruler, ho. (It doesn’t matter whether you measure ho from the table or the base of the ruler since we are only using a difference in heights). Gently push the plates together until they touch. Record the new height of the laser on the ruler, htouch. The geometry of bouncing a beam off the mirror gives the plate

separation as  o o touch X

y h h 2D

   . Calculate yo in your Excel spreadsheet, being careful to use

meters for all distances. Check to see if your laser measurement of the separation between the plates is close to the distance you measured with a ruler in part 1.

3. MEASURE DEFLECTION VERSUS MASS

With the power supply still off:

3.1. PLACE MASSES ON THE PANS Place just enough mass on the center of the pan so that the distance between the plates is about one half of the original separation (yo). The mass must be at the center of the pan, so it is at the

Figure 4. Voltmeter

Voltmeter

com

1000 V

To do calculations in Excel, it is helpful to set up a table of variables. Enter “ho” in A1 and enter the value of ho in A2. Enter “htouch” in B1, and enter its value in B2. Enter “X” and “D” in C1 and D1 and enter their values in C2 and D2. Enter “y” in F1. In F2, do the calculation by entering “=(A2-B2)*C2/(2*D2)”.

PHY109 Lab 1 Electric Force Balance

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distance X from the knife edge. Record the mass m1 and compute the force F1=m1g. Read h1 on the meter stick and (in

Excel) calculate  1 1 touch X

y h h 2D

   .

3.2. REPEAT WITH SAME MASS Take the mass off the pan and then repeat 3.1 two more times, to determine the average and standard deviation of y1.

3.3. REPEAT TWICE WITH DIFFERENT MASSES Repeat 3.1 and 3.2 with less mass, so that the distance between the plates is about two-thirds of the original separation (the exact separation isn’t critical). Find F2, h2, and y2 . Repeat again with even less mass. Find F3, h3, and y3.

4. MEASURE DEFLECTION VERSUS VOLTAGE Purpose: From your measurements of deflection vs voltage and deflection versus mass you can

determine the force associated with the voltage and hence estimate o, the fundamental dielectric constant of vacuum.

To avoid electrocuting yourself or your partner: NEVER TOUCH THE APPARATUS WHILE THE VOLTAGE IS ON.

If the plates touch while the power on, they will stick together. Turn off the voltage and they will come unstuck.

Set the voltage to zero before turning on the power source.

4.1. FIND V1 SLOWLY adjust the voltage until the laser spot is at h1 from part 3.1.In Excel record the voltage V1.

4.2. COMPUTE O When V = V1 the electric force magnitude equals F1, so

2

0 1 1 1 2

1

AV F m g

2y

   and therefore

2

1 1 0 2

1

2y m g

AV   .

4.3. FIND V2 AND V3 Adjust the voltage until the laser spot is at h2 and then h3.Record the voltages V2 and V3 and

recalculate o for each voltage.

4.4. COMPUTE THE AVERAGE O AND ITS UNCERTAINTY Compute the average and standard deviation of the three values of o. Compare it to the theoretical value (see page one of this lab). In your report you will address any discrepancies between your

measured and the theoretical values of o. Before you leave today you may want to take a moment to think about what sources of error affected your calculations and how significant they may have been.

If the deflection is not repeatable, gently push the plates together and let it return to equilibrium. If necessary, use the knurled knob to lift the plate and re-center the knife edges (if you do this you should re-measure ho , htouch and yo).

PHY109 Lab 1 Electric Force Balance

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LAB REPORT QUESTIONS Each question needs to be answered in a separate paragraph in the results section of your report. If you are not continuing from Physics Lab 1, and have never written a physics lab report before, you should read the lab report guides on Blackboard before starting your report.

1. With the power off, what distance did you measure for the separation between the two plates using a ruler (section 1.1) and using the laser method (section 2). Do they agree? Why or why not?

2. For each of the separations of the plates you measured, list the masses and corresponding voltages (ie. y1, m1 and V1). Why did you need greater voltages for the larger masses?

3. Based on the data you collected in lab what was your calculated value of o? Would you say your result agrees with the theoretical value? Why or why not? What sort of factors do you believe may

have contributed to any error between your result and theoretical value of o?

PRE-LAB QUESTIONS

While there is no pre-lab for this lab, you are strongly advised to read the entire lab before doing it, with an emphasis on understanding which values you will be calculating and why, and how they will be used algebraically to calculate the permittivity constant. For this and all labs you should also read the lab report questions in advance so you know what will be expected of you in your report.