AP Physics C E&M 8.1.C: Electric Permittivity

Practise AP Physics C E&M 8.1.C by using a capacitance graph's y-intercept and plate dimensions to calculate the permittivity of free space.

[Maximum number: 2]

Students design an experiment to determine the unknown dielectric constant $\kappa$ of a plastic material.

A capacitor is created using two square aluminum plates of side length $s=30 \mathrm{~cm}$ that are separated by

a distance $d=1.0 \mathrm{~mm}$ . This capacitor is placed in a circuit with an ideal 6.0-volt battery, a resistor of resistance

$R=500 \Omega$ , voltmeter V, and an open switch S, as shown above. A1.0 mm thick piece of plastic is inserted

between the aluminum plates. The distance x that the plastic is inserted between the plates can be varied, and the

voltmeter is used to measure the potential difference $V_{C}$ across the capacitor. The switch is closed, and readings

from the voltmeter are recorded as a function of time t. The data are plotted to create the graph shown below.

Figure for Question 8.1.C—Describe the electric permittivity of a material or medium question 1 — AP Physics C: Electricity & Magnetism

The time $t_{1 / 2}$ shown above is the time for the capacitor to charge to half the potential difference of the battery.

The students now want to verify the value for the permittivity constant, $\varepsilon_{0}$ . Using the graph from part (b),

calculate an experimental value for $\varepsilon_{0}$ .

CNV-7.A.a, SP 4.D, 6.C

2 points

The students now want to verify the value for the permittivity constant, $\varepsilon_{0}$ . Using the graph from

part (b), calculate an experimental value for $\varepsilon_{0}$ .

\begin{tabular}[t]{|l|l|}
\hline For using an acceptable value for the y-intercept consistent with the best-fit line

1 point

For correctly relating the y-intercept to the permittivity constant

1 point

$C=\frac{\varepsilon_{0} s^{2}}{d}+\frac{\varepsilon_{0} s(\kappa-1)}{d} x \therefore$ y-intercept $=\frac{\varepsilon_{0} s^{2}}{d}$ $\varepsilon_{0}=\frac{(d)(\mathrm{y} \text {-intercept })}{s^{2}}=\frac{\left(1 \times 10^{-3} \mathrm{~m}\right)\left(8.4 \times 10^{-10} \mathrm{~F}\right)}{(.3 \mathrm{~m})^{2}}=9.29 \times 10^{-12} \mathrm{C}^{2} /\left(\mathrm{N} \cdot \mathrm{m}^{2}\right)$

Units point

CNV-7.A.a, SP 7.A1 point

\begin{tabular}[t]{|l|l|}
\hline For correct units in parts (d) and (e)

1 point

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8.1.C—Describe the electric permittivity of a material or medium question 1