Ceramic insulators often display a permittivity that depends on temperature

PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance

Problem

T

. A laboratory sample of a ceramic with empirical relative permittivity data is shown in the table.

Temperature $T$ ( $^\circ\text{C}$ )	$\varepsilon_{r}$
20	1200
40	1140
60	1080
80	1020
100	970

+2.5\,\mu\text{C}

point charge is fixed at one corner of a cubic cavity carved in a large block of the ceramic. A second point charge of

-2.5\,\mu\text{C}

is fixed at the opposite corner of the cavity,

0.12\,\text{m}

away. The cavity is small enough that edge effects can be ignored and the space between the charges is completely filled with the ceramic. Use the information provided to analyze the force between the charges as the temperature changes. (a) Using an appropriate method, estimate the relative permittivity of the ceramic at

T=70\,^{\circ}\text{C}

. (b) Calculate the magnitude of the electrostatic force between the charges at

20\,^{\circ}\text{C}

and at

70\,^{\circ}\text{C}

. Clearly show your reasoning. (c) Determine the percent change in the force magnitude between the two temperatures. (d) Discuss how temperature-induced changes in atomic polarization could produce the trend observed in the table.

Related theory

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