[Electromagnetism] How much work is required in moving Q3 to infinity?

[Sean1218]

Homework Statement

How much work is required in moving Q3 to infinity while Q1 and Q2 remain in their positions?

Q3-------a-------|
|-----------------| b
Q1-------------Q2

a = 16.0 cm
b = 6.0 cm
Q1 = 5.70 μC
Q2 = -5.70 μC
Q3 = 1.8 μC

Homework Equations

W=ΔPE
PE=kQ1Q2/r

The Attempt at a Solution

Just added the potential energies associated with Q3 which is the work needed to move Q3 to infinity (i.e. bring said potential energies to 0).
kQ1Q3/r₁₃ + kQ2Q3/r₂₃
=(8.9875e9)(5.7e(-6))(1.80e(-6))/0.06 + (8.9875e9)(-5.7e(-6))(1.8e(-6))/sqrt(0.06^2 + 0.16^2)
=0.997 J

Also tried calculating ΔPE = final - initial (I think I messed up the formula, but somehow I got the negative of the first one)
(8.9875e9)(5.7e(-6))(-5.7e(-6))/.16 + 0.827790168702400828475759973771078927721678492943077184393)
= -0.997 J

Trying ΔPE again:
kQ1Q2/r₁₂ - (kQ1Q3/r₁₃ + kQ2Q3/r₂₃ + kQ1Q2/r₁₂)
=-kQ1Q3/r₁₃ - kQ2Q3/r₂₃
=-(8.9875e9)(5.7e(-6))(1.8e(-6))/0.06 - (8.9875e9)(-5.7e(-6))(1.8e(-6))/sqrt(0.06^2 + 0.16^2)
= -0.997 J

What am I supposed to do? Neither of these work.

 

[Redbelly98]

Homework Equations

W=ΔPE
PE=kQ1Q2/r

Yes. And you realize ΔPE is PE_final - PE_initial, right?

The Attempt at a Solution

Just added the potential energies associated with Q3 which is the work needed to move Q3 to infinity (i.e. bring said potential energies to 0).

No, the work needed is ΔPE, which is PE_final - PE_initial.

kQ1Q3/r₁₃ + kQ2Q3/r₂₃
=(8.9875e9)(5.7e(-6))(1.80e(-6))/0.06 + (8.9875e9)(-5.7e(-6))(1.8e(-6))/sqrt(0.06^2 + 0.16^2)
=0.997 J

You have calculated PE_initial here. You want PE_final-PE_initial.

Also tried calculating ΔPE = final - initial (I think I messed up the formula, but somehow I got the negative of the first one)
(8.9875e9)(5.7e(-6))(-5.7e(-6))/.16 + 0.827790168702400828475759973771078927721678492943077184393)
= -0.997 J

Trying ΔPE again:
kQ1Q2/r₁₂ - (kQ1Q3/r₁₃ + kQ2Q3/r₂₃ + kQ1Q2/r₁₂)
=-kQ1Q3/r₁₃ - kQ2Q3/r₂₃
=-(8.9875e9)(5.7e(-6))(1.8e(-6))/0.06 - (8.9875e9)(-5.7e(-6))(1.8e(-6))/sqrt(0.06^2 + 0.16^2)
= -0.997 J
What am I supposed to do? Neither of these work.

Your second answer (the negative one) looks correct to me. However if I use a rounded-off version of k, 8.99e9 N*m²/C², then the answer rounds off to -0.998 J.

p.s. please don't report results, even intermediate calculations, to 50 significant figures. It just clutters up your work unnecessarily for people who are trying to follow your calculation.

 

[Spinnor]

Are you submitting this to a computer? I'm not sure how many significant digits your answer should have, but have you tried -1.0?