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Lo.Lee.Ta.
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1. A system consists of the charges -q at (-d,0), +2q at (d,0), and +3q at (0,d). What is the total electric potential energy of the system.
2. I'm wondering, is it necessary to calculate each electric potential between charges from lower electron potential to higher electron potential?
-V-q to +3q = [itex]\frac{k(-q)}{\sqrt{2}d}[/itex] + [itex]\frac{k(+3q)}{\sqrt{2}d}[/itex]
V= -[itex]\frac{2kq}{\sqrt{2}d}[/itex]
-V-q to +2q = [itex]\frac{k(-q)}{2d}[/itex] + [itex]\frac{k(+2q)}{2d}[/itex]
V= -[itex]\frac{kq}{2d}[/itex]
-V+2q to +3q = [itex]\frac{k(+2q)}{\sqrt{2}d}[/itex] + [itex]\frac{k(+3q)}{\sqrt{2}d}[/itex]
V= -[itex]\frac{5kq}{2d}[/itex]
The book solution says this last V should equal positive [itex]\frac{k(2q)(3q)}{\sqrt{2}d}[/itex]...
But more simplified, that would equal: 6q2k/[itex]\sqrt{2}[/itex]d
So, how did they get this? And- why is it positive?
I thought that if we have low electric potential to high electric potential, then ΔV= (-)
(Va - Vb = ΔV = low - high = a NEGATIVE number)
In the first 2 calculations, we went from -q to +2q and -q to +3q.
So this means we went from LOW potential to HIGH potential. So it would make sense that these two V values are negative.
But the third also goes from lower to higher potential (+2q to +3q)... So why isn't this one also negative...?
#=_= So confused.
Please help? Thanks! :)
2. I'm wondering, is it necessary to calculate each electric potential between charges from lower electron potential to higher electron potential?
-V-q to +3q = [itex]\frac{k(-q)}{\sqrt{2}d}[/itex] + [itex]\frac{k(+3q)}{\sqrt{2}d}[/itex]
V= -[itex]\frac{2kq}{\sqrt{2}d}[/itex]
-V-q to +2q = [itex]\frac{k(-q)}{2d}[/itex] + [itex]\frac{k(+2q)}{2d}[/itex]
V= -[itex]\frac{kq}{2d}[/itex]
-V+2q to +3q = [itex]\frac{k(+2q)}{\sqrt{2}d}[/itex] + [itex]\frac{k(+3q)}{\sqrt{2}d}[/itex]
V= -[itex]\frac{5kq}{2d}[/itex]
The book solution says this last V should equal positive [itex]\frac{k(2q)(3q)}{\sqrt{2}d}[/itex]...
But more simplified, that would equal: 6q2k/[itex]\sqrt{2}[/itex]d
So, how did they get this? And- why is it positive?
I thought that if we have low electric potential to high electric potential, then ΔV= (-)
(Va - Vb = ΔV = low - high = a NEGATIVE number)
In the first 2 calculations, we went from -q to +2q and -q to +3q.
So this means we went from LOW potential to HIGH potential. So it would make sense that these two V values are negative.
But the third also goes from lower to higher potential (+2q to +3q)... So why isn't this one also negative...?
#=_= So confused.
Please help? Thanks! :)