Lab 2 - Plotting of Potential Fields Eric Tao January 28th...

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Plotting of Potential Fields Eric Tao January 28th, 2013 Abstract Electrical fields caused by a charge will vary based on, theoretically, only the charge and distance. However, at close enough distances to a surface charge, the geometry of the charge will start to dominate. This study determines a number of the electrical equipotential lines around charges with a given voltage difference, using a voltmeter and power supply. From this, we can extrapolate the potential lines around most geometric figures. 1 Introduction From the formula of Coulomb’s Law, we know that the force felt between two charges is equal to F = q 1 q 2 r 2 . However, if we then consider the force felt on one of the particles, when its charge q 2 is q 1 , then we find that the force exerted on it goes as q 2 r 2 . This provides the basis, then, for the concept of an electrical field. We define the electrical field as F e q 2 , eliminating the arbitrary second charge from our equation. Thus, we may think of an electrical field as a measurement of how any charge will behave when placed nearby, due to the field exerted by our measured charged particle. This can be likened to a gravitational field, replacing charges with masses. However, this view works only for a test charge q 2 sufficiently small as to not create a significant electrical field of its own; in that case, the two fields would interact, creating a more complex field arrangement. One method of measuring the field would be to drop test charges into the field and then observing with what accleration it moves, and in what direction. This assumes that test charges have a minimal charge, so as to not disturb the overall integrity of the field. Alternatively, we may think of an electrical field as having some energy contained within it. Thus, to move with or against the electrical field will constitute a change in energy. Then, by plotting the potential fields, we may then extrapolate the electrical fields, as they must lie perpendicularly. (Mathematically, we may represent this as E ∝ ∇ φ ) In that case then, by measuring the lines of equal potentials, that is, the lines in which it takes no extra work to move along, we may then find the electrical field lines by finding the perpendiculars. This is
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