💡AP Physics C: E&M
3. A student is asked to determine the electric permittivity of an unknown dielectric material by measuring the electric field between two oppositely charged parallel conducting plates separated by a fixed distance.
Describe a procedure for collecting data that would allow the student to determine the relative permittivity κ of the dielectric slab. Your procedure should include (i) what quantities will be measured and how each will be measured using the available equipment, and (ii) at least one specific method for reducing experimental uncertainty (for example, multiple trials and averaging or systematic variation of an independent variable).
Describe how the collected data could be graphed and how that graph would be analyzed to determine κ. In your description, include a mathematical expression that relates the graph's slope (or slopes) to κ. Assume the electric field magnitude between the plates is E = V/d in air and E = V/(κd) when the dielectric fills the space.
Figure 1. Parallel-plate apparatus with sphere
Figure 2. Apparatus with dielectric slab
Figure 3. Blank grid for graphing
V (V) | θ_air (deg) | θ_d (deg) |
|---|---|---|
100 | 7.1 | 5.2 |
200 | 14.0 | 10.4 |
300 | 20.5 | 15.6 |
400 | 26.3 | 20.6 |
500 | 31.6 | 25.5 |
The student performs trials both with air between the plates and with the dielectric slab inserted as shown in Figure 2. For each applied potential difference V, the student measures the equilibrium angle θ of the suspended charged sphere relative to the vertical. The plate separation is d = 0.020 m and the sphere's mass is m = 0.0150 kg. The measured angles are shown in Table 1.
Indicate two quantities, either measured quantities from Table 1 or additional calculated quantities, that could be graphed to produce a straight line that could be used to determine κ.
Vertical axis: Horizontal axis:
On the grid provided in Figure 3, create a graph of the quantities indicated in part C(i).
Use Table 2 to record the measured or calculated quantities that you will plot.
Clearly label the axes, including units as appropriate.
Plot the points you recorded in Table 2.
Draw a best-fit line for the data graphed in part C(ii).
Using the best-fit line that you drew in part C(iii), calculate an experimental value for the relative permittivity κ of the dielectric slab. In your calculation, determine the slope using two points on your best-fit line and use a mathematical relationship that connects that slope to κ.
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