686_PartUniversity Physics Solution

686_PartUniversity Physics Solution - Electric Potential...

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Electric Potential 23-9 (d) The graph of V versus x is sketched in Figure 23.22b. Figure 23.22b EVALUATE: (e) When 0 12 , , 4 q xa V x π >> = P just like a point charge of charge 2. q + At distances from the charges much greater than their separation, the two charges act like a single point charge. 23.23. IDENTIFY: For a point charge, kq V r = . The total potential at any point is the algebraic sum of the potentials of the two charges. SET UP: (a) The positions of the two charges are shown in Figure 23.23. EXECUTE: (b) () 0. kq k q V rr =+ = (c) The potential along the x -axis is always zero, so a graph would be flat. (d) If the two charges are interchanged, then the results of (b) and (c) still hold. The potential is zero. EVALUATE: The potential is zero at any point on the x -axis because any point on the x -axis is equidistant from the two charges. Figure 23.23 23.24. IDENTIFY: For a point charge, kq V r = . The total potential at any point is the algebraic sum of the potentials of the two charges. SET UP: Consider the distances from the point on the y -axis to each charge for the three regions aya −≤ ≤ (between the two charges), ya > (above both charges) and < − (below both charges). EXECUTE: (a) 22 2 || : . kq kq kqy V ay ay y a <= = +−− 2 : kq kq kqa yaV ay yay a >= = . 2 : ( ) kq kq kqa V ay ya y a <− = = +− + . A general expression valid for any y is || qq Vk ⎛⎞ ⎜⎟ −+ ⎝⎠ . (b) The graph of V versus y is sketched in Figure 23.24. (c) 2 :. kqa kqa V y −− >> = (d) If the charges are interchanged, then the potential is of the opposite sign.
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23-10 Chapter 23 EVALUATE: 0 V = at 0 y = . V →+∞ as the positive charge is approached and V →−∞ as the negative charge is approached. Figure 23.24 23.25. IDENTIFY: For a point charge, kq V r = . The total potential at any point is the algebraic sum of the potentials of the two charges. SET UP: (a) The positions of the two charges are shown in Figure 23.25a. Figure 23.25a (b) 2( ) :. () kq kq kq x a xaV x xa x xa −+ >= = −− 3 ) 0: . kq kq kq x a x ax x << = − = ) . kq kq kq x a xV x xa x <= + = A general expression valid for any y is 2 || | | qq Vk x ⎛⎞ =− ⎜⎟ ⎝⎠ . (c) The potential is zero at and /3. x aa (d) The graph of V versus x is sketched in Figure 23.25b. Figure 23.25b EVALUATE: (e) For 2 :, kqx kq V x x >> = which is the same as the potential of a point charge – q . Far from the two charges they appear to be a point charge with a charge that is the algebraic sum of their two charges.
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Electric Potential 23-11 23.26. IDENTIFY: For a point charge, kq V r = . The total potential at any point is the algebraic sum of the potentials of the two charges.
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This note was uploaded on 07/16/2011 for the course PHY 2053 taught by Professor Buchler during the Spring '06 term at University of Florida.

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686_PartUniversity Physics Solution - Electric Potential...

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