Three point charges are on the x axis: q 1 is at the origin, q 2 is at x = +3.7

Question

Three point charges are on the x axis: q1 is at the origin, q2 is at x = +3.7 m, and q3 is at x = +5.1 m. Find the electrostatic potential energy of this system of charges for the following charge values. (Assume the potential energy is zero when the charges are very far from each other.)

1)

q1 = q2 = q3 = +2.7 µC
mJ

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2)

q1 = q2 = +3.3 µC and q3 = -3.3 µC
mJ

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3)

q1 = q3 = 3.7 µC and q2 = -3.7 µC

mJ

Explanation / Answer

U = kq1q2/r12 + kq1q3/r13 + kq2q3/r23

here r12 = 3.7 m

r13 = 5.1 m

r23 = 1.4 m

k = 9 x 10^9

part 1)

q1 = q2 = q3 = 2.7 x 10^-6 C

U = kq^2[1/r12+1/r13+1/23]

U = 0.07746 J = 77.46 mJ

part 2)

q1 =q2 = +3.3 x 10^-6 C

q3 = -3.3 x 10^-6 C

U = k[q1q2/r12 + kq1q3/r13 + kq2q3/r23]

since magnitude of every charge is equal

U = kq^2[1/r12 - 1/r13 - 1/r23]

U = -0.0627 J = -62.7 mJ

part 3 )

q1 = q3 = 3.7 x 10^-6 ,q2 = -3.7 x 10^-6

U = kq^2[-1/12 + 1/r13 - 1/r23 ]

U = -0.09715 J = -97.15 mJ

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