Question

Chapter 24, Problem 044 Your answer is partially correct. Try Your answer is partially correct. Try again. In the figure seven charged particles are fixed in place to form a square with an edge length of 2.7 cm. How much work must we do to bring a particle of charge +5e initially at rest from an infinite distance to the center of the square? -9e +3e Number Units [J

Answer 1

Work-done is given by:

W = dPE

W = PEf - PEi = PEf

Since PEi = 0, at infinity

W = PEf = Potential energy due to all 7 charges at the center

W = PE1 + PE2 + PE3 + PE4 + PE5 + PE6 + PE7

PE is given by:

PE = kq1q2/r

for 4 charges on corners r1 = r2 = r3 = r4 = r

for 3 charge on mid-points r5 = r6 = r7 = 2.7/2 = 1.35 cm = 0.0135

W = kq1*q/r1 + kq2*q/r2 + kq3*q/r3 + kq4*q/r4 + kq5*q/r5 + kq6*q/r6 + kq7*q/r7

q = +5e

W = k*3e*5e/r + k*e*5e/r + k*(-3e)*5e/r + k*(-e)*5e/r + k*3e*5e/0.0135 + k*(-2e)*5e/0.0135 + k*2e*5e/0.0135

Initial 4 quantities will sum up to zero and last two quantites will also sum up to zero.

W = k*15*e^2/0.0135

W = 9*10^9*15*(1.6*10^-19)^2/(0.0135)

W = 2.56*10^-25 J

Please Upvote.