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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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