Question about sign notation

[Raiden2012]

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Hey all,

So the question is what is the work done by a positive charge when a negative charge is brought closer to it.

Would the work done be negative since it is 2 opposite charges?

The answer states it's positive but doesn't provided any explanation.

Thanks!

 

[milski]

The work done on the negative charge by the positive charge is positive - the direction of movement and the direction of the force doing the work are the same.

 

[Raiden2012]

Thanks but I still don't get it. Correct me if I'm wrong but the equation for energy is the (q_1 * q_2)/r
Since they are opposite charges, the energy should be negative no?

So if the two charges were positive instead and 1 was brought closer to the other, would the energy still be positive? Or negative?

 

[milski]

Which energy are we talking about? PE of the negative charge? Yes, it will be negative in the case of opposite charges and will decrease when the charges get closer. But you cannot claim that W=ΔPE in this case.

Consider work from its simple definition F.d - the force and the displacement in this case do have the same sign.

 

[Raiden2012]

Thanks, this makes sense now. I was assuming what you mentioned. Should have gone to basics rather try to equate the 2.

 

[milski]

The energy transfer in what you describe is more convoluted that it seems at first glance, especially if the negatively charged particle was at rest in its original and final position. Even in the simple case, where it moves unrestricted, all that you can say is that W+ΔPE+ΔΚΕ=0 which makes it harder to say anything about the sign of W directly from this equation.

 

[Raiden2012]

Which makes me wonder

The work that is being done is being used to do what exactly? Raise internal energy? Cause the potential energy is probably being exchanged for kinetic energy