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Page 2 - 3 A point charge exists at the origin of a...

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Unformatted text preview: 3.) A point charge exists at the origin of a coordinate axis. A distance 2 meters down the x axis, the electric field is observed to be 12 nt/C. a.) What is the electrical potential at that point? Sim: The electric field function for a point mass is kQ/rz, whereas the electrical potential function for a point charge is kQ/r. As the r terms are the same in both cases (i.e., the distance between the field producing charge and the point of interest), the electrical potential expression is evidently just r times E in this case. That means the electrical potential is (12 nt/C)(2 meters) = 24 volts. (Note that a nt-m is an energy quantity, and energy divided by Coulombs is a volt.) b.) You double the distance to 4 meters. i.) What is the new electric field? Wu: The electric field is a function of 1/r2. Doubling :- will change the electric field by a factor of 1/(2)2 = 1/4. ii.) What is the new electrical potential? 52mg: The electrical potential is a function of Ur. Doubling r will change the electrical potential by a factor of 1/2. Equipotential lines 4.) You have an electric field as shown. What will equipotential lines look like in the field? 5.9km: An equipotential line is a line upon which the electrical potential is the same at every point. It turns out that equipotential lines cut across electric field lines at right angles. So, for electric field lines to the right, the associated equipotential lines would be up and down (see sketch). 5.) How is the electrical potential difference between two points related to the amount of work required to move a charge q from one point to the other? Milan: By definition, W/q = - AV, so W: -q AV. 6.) The dotted lines in the sketch to the right are electric field lines. Shown also are the 1 volt and 2 volt equipotential lines. Draw in the 3 volt and 4 volt 1v_l__.—" equipotential lines. it """"""""""" > ‘ mm: What's tricky here is the fact that as the electric _ field weakens, the equipotential lines get farther apart. This ‘2‘ follows both mathematically and logically. Mathematically, the relationship E-d = - AV suggests that if E gets smaller (this V is what happens as the electric field lines get farther apart), the distance d between incremental equipotential lines must get larger if the voltage change is to stay the same. From a common sense perspective, if 114 ...
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