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Chapter 20: Problem 61

A molecule has its dipole moment aligned with a 1.2 -kN/C electric field. If it takes \(3.1 \times 10^{-27} \mathrm{J}\) to reverse the molecule's orientation, what's its dipole moment?

Short Answer

Expert verified
The dipole moment of the molecule is approximately \(1.29 \times 10^{-24}\) C·m.

Step by step solution

01

Interpret the Given Values

In this exercise, we have the following known values: the electric field strength \(E = 1.2 \, \mathrm{kN/C} = 1.2 \times 10^{3} \, \mathrm{N/C}\) (1 kN/C is equal to \(10^{3}\) N/C) and the work \(W = 3.1 \times 10^{-27} \, \mathrm{J}\) needed to reverse the molecule's orientation. These will be needed to solve the problem.
02

Understand the Physics Concept

The work done to reverse a dipole’s orientation in an electric field is equal to the change in potential energy, which is given by the equation: \( \Delta U = pE \cos \theta - (-pE \cos \theta) = 2pE\), where \(p\) is the dipole moment, \(E\) the electric field and \(\theta\) the angle between the dipole moment and the electric field. In this case, \(\theta = 180°\), therefore, \(\Delta U = 2pE\).
03

Calculate the Dipole Moment

Substitute the values of the change in potential energy and the electric field into the equation \( \Delta U = 2pE\) and solve it for the dipole moment \(p\): \(p = \Delta U / 2E = (3.1 \times 10^{-27} \, \mathrm{J}) / (2 \times 1.2 \times 10^{3} \, \mathrm{N/C})\).

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Most popular questions from this chapter

Protons and neutrons are made from combinations of the two most common quarks, the \(u\) quark (charge \(+\frac{2}{3} e\) ) and the \(d\) quark (charge \(-\frac{1}{3} e\) ). How could three of these quarks combine to make (a) a proton and (b) a neutron?

How strong an electric field is needed to accelerate electrons in an X-ray tube from rest to one-tenth the speed of light in a distance of \(5.0 \mathrm{cm} ?\)

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