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# CH 19 Notes - C H 19 Electric Potential Energy and the...

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CH 19. Electric Potential Energy and the Electric Potential Electrostatic Potential Energy is very useful for studying the motion of charged particles in electric fields. Potential Energy o Work is done by gravitational force mg as the ball falls from A to B (fig. 1). W AB = GPE A - GPE B = mgh A - mgh B o Work is done by electric force q 0 E as positively charged particles move from A to B (fig. 2). W AB = EPE A - EPE B = q 0 E S A - q 0 E S B = q 0 V A - q 0 V B Electric Potential Difference o Electric potential: The electric potential at a given point is the electric potential energy of a small test charge divided by the charge itself: V = EPE/q 0 V (J/C) * 1 V = 1 J/C * The electric potential V is a scalar quantity. o The positive charge accelerates as it moves from A to B (fig. 2) because of the electric repulsion from the upper plate and the electrical attraction from the lower plate. Thus we must conclude that a positive charge accelerates from a region of higher electric potential toward a region of lower electric potential. On the other hand, a negative charge accelerates from a region of lower electric potential toward a region of higher electric potential. o Often the voltage difference (final value minus initial value) in potentials is used, so

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V B - V A = EPE B /q 0 – EPE A /q 0 = - W AB /q 0 V = (EPE)/q Δ Δ 0 = - W AB /q 0 Ex. 1 : The work done by the electric field as the test charge (+2.0x10 -6 C) moves from A to B is +3.0x10 -5 J. (a) Find the difference in EPE between these points (A – B) (b) Determine the potential difference between these points (final minus initial) (fig. 3). Conceptual Ex. 2: A positive test charge is released from A and accelerates towards B. Upon reaching B, the test charge continues to accelerate towards C. Assuming that only motion along the lines is possible, what will a negative test charge do when released from rest at B? (fig. 4). o While SI unit for electric potential energy EPE is joule (= C/V) often one uses electron volt when working with charged particles. o One electron volt is the magnitude of the amount by which the potential energy of an electron changes when the electron moves through a potential difference of one volt. 1 eV = 1.60x10 -19 V Conservation of Energy o Alternatively, use Conservation of Energy equation with the gravitational and electric potential energies to understand the motion: (fig. 2). KE A + EPE A = KE B + EPE B (½)mv 2 A + q 0 V A = (½)mv 2 B + q 0 V B
Ex. 3: A particle has a mass of 1.8e-5 kg and a charge of +3.0e-5 C. It is released from point A and accelerates horizontally until it reaches point B. The only force acting on the particle is the electric force generated by the electric potential at A being 25 V greater than at B.

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