Charge q1 = 9.5 nC is located at the coordinate system origin, while charge q2 =
ID: 582655 • Letter: C
Question
Charge q1 = 9.5 nC is located at the coordinate system origin, while charge q2 = 0.43 nC is located at (a, 0), where a = 0.55 m. The point P has coordinates (a, b), where b = 0.65 m. A third charge q3 = 2.5 nC will be placed later.
A) Find the electric potential VP at point P, in volts. Assume the potential is zero at infinity. B) How much work W, in joules, would you have to do to bring the third charge, q3, from very far away to the point P? C) What is the total potential energy U, in joules, of the final configuration of three charges?
(a,b) qi qi 2Explanation / Answer
potential due to charge at point P = Kq1/r1 + Kq2/r2
r1 and r2 are the distances from point to the charges.
Potential due charge q1 = K*9.5* 10^ -9 / sqrt(0.55^2 + 0.65^2) = 100.30 V
Potential due to chrge q2 = K *0.43*10^-9/ 0.65 = 5.95 V
net potential at point P = 100.30 + 7.036 = 106.25 V
B.) work done = change in potential energy = Q3* V- 0 = 2.5*10^-9 * 106.25 - 0 = 2.65 * 10^-7 J
c.)
potentail energy of final configuration = U12 + U23 + U31
U12 = KQ1Q2 / r = 9*10^9 * 9.5*0.43*10^-18 / 0.55 = 6.68*10^-8 J
U23 = KQ2Q3 /r = 9*10^9*0.43*2.5*10^-18 / 0.65 = 1.488*10^-8 J
U31 = KQ3Q1 /r = 9*10^9*2.5*9.5*10^-18 / 0.851 = 2.5 * 10^ -7 J
total potential = 3.31*10^-7 J