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}Summary In this lesson, the focus was on electric potential from point sources. Just as the gravitational potential energy between two masses is givenby pg _ G mm, , similarly the electric potential energy between two point r i i _ .49 charges is found using PEc k-;-- . The "zero" of potential energy occurs when the point charges are at an infinite separation distance. If the two point charges have the same sign, then more potential energy is stored as they move close together, and the potential energy rises. If the two charges are opposite in sign, then there is less potential energy between them, in fact we can say that the potential energy becomes more negative. If we simply use the symbol g to mean the charge producing the electric potential at a given location, then the general form for electric potential created by a point charge can be written as V=rk 4 The units for electric potential for a point charge remain volts. r When two or more charges are present, the potential due to all the charges is obtained by adding together the individual potentials. A positive point charge has electric field lines that radiate out from it. The lines of equipotential would form circles at a given fixed radius out from the charge. In the case of two or more charges, the lines of equipotential remain perpendicular to the electric field lines. Question(s): The physics of electric potential energy at one corner of a triangle. Two charges, g1 = +5.0 pC and g5 = -2.0 uC are 0.50 m apart. A third charge, g3 = +6.0 uC is brought from infinity to a spot 0.50 m from both charges so that the three charges form an equilateral triangle. 1. Determine the total electrical potential at the location of g3 created by the charges g1 and g. 2. Determine the change in electric potential energy in bringing the charge g3 to this location. 3. Determine the work required to bring the charge g3 to the location described. ),9};3 Electric Potential for a Negative Point Charge When the point charge is negative, the potential at infinity is still zero, but as the negative charge is approached, the potential becomes more and more negative. rs Fa | V'_ 0 atr= '\\ higher potential lower potential v If the point charge had a magnitude of -4.0 x 108 C, the electric potential at a point 10.0 m away from it would be -8 =8.99x10N- mZ/CZ(%J =36V At a distance of 1.0 m, the electric potential would be -360 V. W= wF UuwWInUau z}? Gravitational Potential Energy for Two Masses Before considering electric potential energy for two point charges, we will review gravitational potential energy. From your study of mechanics, you may recall that the force of attraction between any two masses m4 and m is given by the equation mm, k=67 r A graphical representation showing the relationship between the gravitational force of attraction and the distance between the masses would look as follows. F, |- " r Just as in the situation described earlier, to find the change in gravitational potential energy between the masses, we would find the area under the curve. For an inverse square relationship, we would need calculus to do this accurately. The result would show that the change in gravitational potential energy is given by APE= Gm!m.._{1 l] L h For two masses separated by the same distance m, the gravitational potential energy stored between them is PE _gT r