A parallel plate capacitor has area A = 47.0 cm2 and a separation of 2.00 m betw

Question

A parallel plate capacitor has area A = 47.0 cm2 and a separation of 2.00 m between the two plates. A single water molecule is placed between the two plates, the water molecule having a dipole moment of p = 6.20E-30 C*m. The capacitor is then charged to a voltage of V = 23.5 V. What is the magnitude of the electric field between the two plates? What is the difference between the maximum and minimum potential energy of the water molecule in this field? What is the ratio of the answer to part (b) and the thermal energy kBT, if kB is Boltzmann's constant, T is the temperature in Kelvin, and the experiment is done just at the freezing point of water? Note that if the answer to part (c) is small compared to 1, the molecules will mostly be random, but if it is large, they will all be aligned with the electric field.

Explanation / Answer

a) E= V/d = 23.5/2um = 11.75 *10^6 N/c

b) potential enery = -P.E

minimum = 0

maximum = 11.75 *10^6 * 6.20E-30 = 7.285 *10 ^-23 Volt

difference = 7.285 *10 ^-23 Volt

c) 7.285 *10 ^-23 / (273 * Kb) = 0.0193

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