Calculate the torsion angle (Dq = q- q0) for each distance. Remember q0 is the average of q01 through q05.
Measure the torsion angle (Dq = q-q0) for separation distances of 25, 20, 17, 14, 12, 10, 8, 6 cm.
Note:
a) Always move the supporting rod by holding it at the bottom.
- Please keep in mind that charges are continuously leaking out into the air. Taking data quickly
will help.
- When the separation is small, the hanging ball will turn too much counter clockwise when doing step 2 above and might touch the aluminum rods thereby losing charge. To avoid this, one person should hold the aluminum plate from turning while another person will charge the balls. It is always a good idea to hold the aluminum plate at its alignment position, so that the plate does not have to turn much when you bring the other charged ball to its position and you can quickly get the alignment position burning the dial, if needed.
- Once you charge the balls, try to keep your hands and body away from the balls as much as possible. Remember, the balance is very sensitive to any air flow including your breath.
- All angles should be positive. If needed, add 360 degrees to a negative angle to make it positive.
Calculate the torsion angle (Dq = q- q0) for each distance. Remember q0 is the average of q01 through q05.
Plot Dq versus r. Question. Is it a straight line? From the nature of the curve can you guess what kind or relation Dq and r will have?
Plot ln Dq (y axis) versus ln r (x-axis) (Equation 4).
From the ln Dq versus ln r plot, note the slope (the “a” in Equation 3b) of the best fit line (use Excel).
Qs. Do you have a better idea about the relationship between Dq and r? Was it necessary to plot the log-log graph to understand the nature of the relationship between Dq and r better? Discuss your opinion.
Note that when the balls are very close, the repulsive force will be higher than when they are further away.
Also note that because of the repulsive force, the charges on one ball will move away from the charges from the other ball causing the effective distances between the two set of charges more than the distances between the centers of the balls. This means that the experimental repulsive force will be less than if the charges were point sources. This requires some correction as the charges are not distributed uniformly around the ping-pong balls and cannot be treated as point sources at the centers of the balls. Table 2 introduces the correction factor (B) for this effect.
In order to correct for the non-point source of charge, consider correcting the value of Dq by dividing it by the factor B, where B=1 – 4(R/r)3 , R = radius of the ball (meter) and r = separation distance between centers the balls (meter) .
Calculate Dq’ = Dq/B and plot ln(Dq’) versus ln (r). Question. Does this give a better value of ‘a’?
Using the data from table 2, plot Dq’ versus 1/r2 and check if the best fit line is a straight line going through the origin.
Qs. Does your data support the prediction from Coulomb’s law that F a r –2 ?
Qs. Why are you not charging the balls keeping them at the separation distances without moving them apart? That would have avoided moving the fixed ball back and forth.
Qs. Why are you not discharging the balls before recharging? Every time you recharge, are you not adding charge on top of the residual charge the balls have causing the charge on the ball to go higher and higher? Explain.
Qs. If the two balls are charged when they are close to each other, will the amount of charge on the two balls be same? Explain.
- Discharge rate:
- Find the alignment angle, q for a separation distance of 6cm with the balls charged at 6kV following part 1. As soon as you get the alignment and note the alignment angle (q), start the stopwatch.
- Immediately, turn the dial clockwise by 10 degrees, which will disturb the alignment. You will notice that as the balls are losing charge, the two reference lines are coming close to each other. When the two lines get aligned, note down the running time and the alignment angle. Do not touch the stopwatch – keep it running.
- Keep on repeating step (b) for around 30 minutes. Finally, you will have a set of alignment angles (q) at various times of discharge (t).
- Plot a graph of torsion angle (Dq=q-q) vs. time. Comment on the shape of the discharge graph. Does it look like an exponential discharge graph? If yes, the draw another graph for ln(Dq) vs. time and find the equation for the best fit straight line. From the slope, Find the time at which each of the balls will discharge 63% of their charge (discharge rate constant = 1/k). Caution: Remember that torsion angles are surrogates for the force between the balls. Here you have to find 1/k from equation 8b.
Qs. Why is ln(Dq) vs. time expected to be linear if you find Dq vs. time is exponential?
- Measure the torsion angle (Dq = q–q0) for various charge:
Follow the method described in part 1 to find the torsion angles for various voltage keeping the separation distance of 6cm for the charging voltage of 2, 3, 4, 5 and 6 kilovolt. (Table 3)
Plot three graphs 1) torsion angle (Dq) vs. voltage (V), 2) torsion angle (Dq) vs (voltage)1/2, and torsion angle (Dq) vs (voltage)2. Question. Is any of these linear? Can you explain the result?
Tables:
Ball diameter = 0.038 meter
Do not forget to provide units.
Table for Average Reference angle (q0):
| Trial # | Reference angle | |
| 1 | q01 | |
| 2 | q02 | |
| 3 | q03 | |
| 4 | q04 | |
| 5 | q05 | |
| 6 | q06 | |
| 7 | q07 | |
| 8 | q08 | |
Average Reference angle = Average of the above five values = q =
Error= range/2 = (maximum – minimum)/2 =
Part 1
Table 1. Torsion angle for various separation distance:
Do not forget to provide units.
| Separation between the balls | Alignment angle | Torsion angle needed to restore alignment | Correction factor | Corrected torsion angle | ||||||
| r (meter) | r2 | 1/r2 | ln( r) | q | Dq= (q-q) | ln(Dq) | B = 1- 4(R/r)3 | Dq’ = Dq/B | ln(Dq’) | |
R = radius of the balls (meter)
Part 2
Table 2: Determination of discharge rate
| Time(t) | q | Dq= q-q0 | ln(Dq) |
Since you do not know how many time points you need in 30 min, you will not know how many rows you should have for this table. So, leave the whole page to take data.
Part 3
Separation distance = 6cm
Table 3: Torsion angle for various charging voltage
| Voltage used (kV) | Alignment angle | Torsion angle needed to restore alignment | |||||||
| V | V0.5 | V2 | q | Dq= (q-q0) | |||||
More Questions:
- If Coulomb’s law is true, why do not the negatively charged electrons in an atom fall to the positively charged nucleus at the center of the atom?
- Again, why do not the positively charged protons in the nucleus fly away from each other due to the repulsion between the like charges?
- After charging the balls and bringing them to a certain separation distance, the hanging ball deflects away. Why don’t we simply measure this angle of deflection with a protractor as a surrogate for the repulsive force instead of turning the dial backward to determine the restoring angle?
- Some foods are very hard to remove from the dishes if they are left to dry out? Why it becomes easier to remove the food once the dishes are soaked in water? Will soaking in other liquids (e.g., oil, gasoline etc.) work?
- Fish easily gets stuck to the frying pan but bean does not. Why?
- If we magnify a hydrogen atom to the size of football field of 100 yards across, what will be the size of the nucleus? Can you calculate roughly what percentage of the atom is ‘empty’?
- With so much emptiness, all materials are essentially empty space and consequently, you should be able to go through a closed door or go through the concrete floor like the ghosts do in the movies. Why then you cannot do that trick in real life?
