1116 EXAMPLE 16.4 Finding the Electric Potential GOAL Calculate the electric pot
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Question
1116 EXAMPLE 16.4 Finding the Electric Potential GOAL Calculate the electric potential due to a collection of point charges. y (m) (0, 400 PROBLEM A 5.00-uC point charge is at the origin, and a point charge q2-_2.00 pC is on the x-axis at (3.00, 0) m, as in the figure. (a) If the electric potential is taken to be zero at infinity, find the electric potential due to these charges at point P with coordinates (0, 4.00) m. (b) How much work is required to bring a third point charge of 4.00 om infinity to P? (3.00,0) point charges The electric potential at point P due to the 41 and 42 is the algebraic sum of the potentials due to tje individual charges STRATEGY For part (a), the electric potential at P due to each charge can be calculated from V keqlr. The electric potential at P is the sum of these two quantities. For part (b), use the work- energy theorem, together with PE, qv, recalling that the potential at infinity is taken to be zero. SOLUTION (a) Find the electric potential at point P. Calculate the electric potential at P due to the 5.00-uC charge. V = ke 91-(8.99 x 109 N·m)(5.00 x 10-6 C c2 4.00 m - 1.12 x 104v Find the electric potential at P due to the -2.00-uC charge V2 = keg2-( 8.99 × 109 N·m?V-2.00 x 10-6 C 5.00 m --0.360x 104 v Sum the two quantities to find the total Yp-Vi + V2-1.12 x 104 V+(-0.360 × 104 V)Explanation / Answer
a)
Potential due to + charge
V1= 9*10^9*4.8*10^-6/4= 10800 V
Potential fue to negative charge
V2= 9*10^9*2.3*10^-6/5 = - 4140 V
Net voltage at P
V= V1+ V2= 10800-4140= 6660 V
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Workdone, W= qV= 3.8*10^-6*6660= 2.53*10^-2 J
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Comment in case any doubt.. good luck
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