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Unformatted text preview: 2/1/2009 1 Motion in a Nonuniform Field An example of this type of motion is the circular orbit of a charged particle around a charged sphere or wire. The fig below shows a negatively charged particle orbiting a positively charged sphere (like the moon orbiting the earth). The electric force here represents the radial force of magnitude, Thus, the charge can move in a circular orbit based on Newtons second law for circular motion if, E q F q on = mv E q 2 = r 26.7 Motion of a Dipole in an Electric Field The polarization force required two steps: 1. An external charge must be used to polarize the neutral object and creates an induced electric dipole. 2. The external charge then exerts an attractive force on the near end of the dipole which is slightly stronger than the repulsive force on the far end. Dipole in an Uniform Field We need to deal with a uniform electric field and that can be achieved by using a field which is created by a parallel-plate capacitor capacitor. Since the two charges of a dipole are equal in magnitude and opposite in charge ( q ), thus the two forces should be equal but opposite. The net force on the dipole is E q F E q F r r r r = + = + and = + = + F F F net r r r 2/1/2009 2 Figure (a) below shows the two forces ( ) acting on a dipole in a uniform electric field. These two forces are equal in magnitude but not aligned with each other. Thus the electric field exerts a torque on the dipole, causes the dipole to rotate until it is aligned with the electric field + F and F r r to rotate until it is aligned with the electric field. In this situation the dipole experiences zero net force and zero net torque. This position called the equilibrium position as shown in fig (b). The two forces on the dipole are called a couple, as shown in the fig below. The torque (twist) due to a couple is given by, sin sin ) )( sin ( pE sqE qE s lF = = = = E p or r r r = where p=sq is the dipole moment, l is the distance b/w the lines of action of the two forces, and is the angle b/w the dipole and the electric field. electric field....
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