An electric dipole consists of two electric charges of equal magnitude and opposite sign. If the charges are q and −q and are located at a distance d from each other, then the electric field E at the point P in the figure is .

By expanding this expression for E as a series in powers of d/D, show that E is approximately proportional to 1/D³ when P is far away from the dipole.

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Supratim PalLv10

22 Dec 2020

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An electric dipole consists of two opposite charges +/- q separated by a small distance (s). The product p=qs is called the dipole moment. The following figure shows an electric dipole perpendicular to an electric field E.(Figure 1)

Find an expression in terms of p and E for the magnitude of the torque that the electric field exerts on the dipole.

silverferret259

Consider an electric dipole whose dipole moment (a vector pointing from the negative charge to the positive charge) is oriented at an angle with respect to the y-axis. There is an external electric field of magnitude E (independent of the field produced by the dipole) pointing in the positive y-direction. The positive and negative ends of the dipole have charges +q and -q, respectively, and the two charges are a distance d apart. The dipole has a moment of inertia I about its center of mass. It will help you to imagine that the dipole is free to rotate about a pivot through its center.

A) What is the net force that the dipole experiences due to the electric field?

B) What is , the magnitude of the torque that the electric field exerts about the center of mass of the dipole?

C) Using the above result, find the potential energy associated with the dipole's orientation in the field as a function of the angle shown in the figure. Take the zero of the potential to occur when the dipole is at angle ; that is , .