Four point charges, each having a charge with a magnitude of 2.2 µC, are at the

Question

Four point charges, each having a charge with a magnitude of 2.2 µC, are at the corners of a square whose sides are 6 m long. Find the electrostatic potential energy of this system under the following conditions.

(a) all of the charges are negative
mJ

(b) three of the charges are positive and one of the charges is negative
mJ

(c) the charges at two adjacent corners are positive and the other two charges are negative
  mJ

(d) the charges at two opposite corners are positive and the other two charges are negative (Assume the potential energy is zero when the point charges are very far from each other.)
mJ

Explanation / Answer

q= 2.2 * 10 ^-6 C
k = 1 / (4 * pi * eo)
r = 6 m
rd = Sqr(6^ 2 + 6^ 2) = 8.485 m

PE1 = (k * q1 * q2) / r 'bring up q2
PE2 = (k * q1 * q3) / rd + (k * q2 * q3 / r) 'bring up q3
PE3 = (k * q1 * q4 / r) + (k * q2 * q4 / rd) + (k * q3 * q4 / r) 'bring up q4
PE = PE1 + PE2 + PE3

(a) all of the charges are negative

PE1 = 0.00726 J

PE2= 0.0124 J

PE3= 0.01965 J
PE = 0.03931 J =39.31 mJ

(b) three of the charges are positive and one is negative (let q1 is negative)

PE1 = -0.00726 J

PE2= 0.002126 J

PE3= 0.00514 J

PE = 0 J

(c) the charges at two adjacent corners are positive and the other two charges are negative

PE1 =  -0.00726 J

PE2= 0.00213 J

PE3= -0.00514

PE = -0.01027 J = -10.27 mJ

(d) the charges at two opposite corners are positive and the other two charges are negative (13 are positive and 24 are negative)

PE1 = - 0.00726 J

PE2= -0.00213 J

PE3= -0.00939 J

PE = - 0.01878 J = -18.78 mJ

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