Well revisit it in a much more similar form when we get to electrostatic

# Well revisit it in a much more similar form when we

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Because one has to integrate over the vectors, this integral is remarkably difficult. We’ll revisit it in a much more similar form when we get to electrostatic potential , a scalar quantity. Electric Dipoles When two electric charges of equal magnitude and opposite sign are bound together, they form an electric dipole . The dipole moment of this arrangement is the source of a characteristic electrostatic field, the dipole field . The dipole moment of the two charges is defined to be: vectorp = q vector l where q is the magnitude of the charge and vector l is the vector that points from the negative charge to the positive charge. When an electric dipole vector p is placed in a uniform electric field vector E , the following expressions describe the force and torque acting on the dipole (which tries to align itself with the applied field): vector F = 0 vector τ = vectorp × vector E Associated with this torque is the following potential energy: U = vector p · vector E and from this, we can see that the force on the dipole in a more general (non-uniform) field should be: vector F = vector U = vector ( vector p · vector E ) which is actually nontrivial to compute. This completes the chapter/week summary. The sections below illuminate these basic facts and illustrate them with examples.
34 Week 1: Discrete Charge and the Electrostatic Field 1.1: Charge In nature we can readily observe electromagnetic forces. In fact, we can do little else. In a very fundamental sense, we are electromagnetism. Electromagnetic forces bind electrons to atomic nuclei, bond atoms together to form molecules, mediate the interactions between molecules that allow them to change and organize and, eventually, live. The energy that is used to support life processes is electromagnetic energy. The objects that we touch, or hear, or taste, or smell, the light that we see, the organized pattern of neural impulses that we use to think about the input from our senses – all are electromagnetic. Given its ubiquity, it should come as no surprise that the directed observation and study of electricity is quite ancient. It was studied, and written about, at least 3000 years ago, and artifacts that may have been primitive electrical batteries have been discovered in the Middle East that date back to perhaps 250 BCE. It is revealing that the very word electricity and the name of the elementary particle most visibly responsible for its transport is derived from the greek word for amber, electron . One of the first recorded observations of electrical force was the static electrical force created between amber, charged by rubbing it with wool, and small bits of wool or hair, although the observation of static sparks and electrostatic forces no doubt predates the written word. However, it took until the Enlightenment (roughly 1600) and the invention of physics and calculus for the scientific method to develop to where systematic studies of the phenomenon could occur, and it wasn’t until the middle 1700s that the correct model for electrical charge 23 was proposed. From