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In regard to electric potentials.
Two charges Q1=Q2=1.1*10^-8C are 2*10^-2 meters apart. Point A is exactly between them, and point B is 10^-1 meters from both of them. How much work is required to move a charge q=10^-9C from A to B?
Va=kQ/da + kQ/da
Va=2*10^4 Nm/C = 2*10^4 V
Vb = kQ/db +kQ/db
Vb= 2*10^3 V
W=q(Vb-Va)
W= -1.8*10^-5 J
It makes sense to me why work is negative, considering the charges Q are both repelling A, but in opposite directions so those forces cancel out. Since point B is far away, the potential is less at point B, and no work is needed to move a charge from higher to lower potential (right?).
However, what does the negative work indicate? Is it just the amount of work necessary to move charge A back to "exactly between" Q1 and Q2 from point B?
The explanation (from NOVA) is this:
I know the answer to my question is the second to last sentence, but I don't understand what it is saying.
Two charges Q1=Q2=1.1*10^-8C are 2*10^-2 meters apart. Point A is exactly between them, and point B is 10^-1 meters from both of them. How much work is required to move a charge q=10^-9C from A to B?
Va=kQ/da + kQ/da
Va=2*10^4 Nm/C = 2*10^4 V
Vb = kQ/db +kQ/db
Vb= 2*10^3 V
W=q(Vb-Va)
W= -1.8*10^-5 J
It makes sense to me why work is negative, considering the charges Q are both repelling A, but in opposite directions so those forces cancel out. Since point B is far away, the potential is less at point B, and no work is needed to move a charge from higher to lower potential (right?).
However, what does the negative work indicate? Is it just the amount of work necessary to move charge A back to "exactly between" Q1 and Q2 from point B?
The explanation (from NOVA) is this:
Since the test charge is positive, we imagine the two charges Q are mountains next to each other, and A is a mountain pass. Point B is further down, so the energy change is negative. No energy is required, but instead energy can be derived. Therefore the negative answer is justified.
I know the answer to my question is the second to last sentence, but I don't understand what it is saying.