Electric potential and work

Hello,

my questions are not really about an exercise or something "given". Instead, I'm having trouble understanding the concepts behind electric potential and work formulae/meaning. Maybe (probably) I missed the basics. Assume that I'm working with a puntiform charge.

1 - I've seen electric potential formulae (using the integral method) appear with and without a negative signal on the integral, and the limits were at the same position in both cases, no inverting at all: what are the differences?

2 - Why is work done by the electric field negative, and the work done by something other than the electric field positive? Wouldn't it make more sense if it was the other way around?

NascentOxygen
Staff Emeritus
1 - I've seen electric potential formulae (using the integral method) appear with and without a negative signal on the integral, and the limits were at the same position in both cases, no inverting at all: what are the differences?

It's all a matter of perspective. If it's a battery that is doing the work, then the battery is depleted of that energy. So a negative would be appropriate for it. For the actuator or heating element, it is work done on it, so positive would seem appropriate.

The nett result, energy sums to zero, meaning no energy was created or destroyed in the process.

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For 1:

It could be for a variety of reasons. It might just mean that in the context only the magnitude of the potential matters, so you would just throw away the negative. It could also be that they do a bit of processing on the inside of the integral -- the integrand involves the dot product of the electric field and the displacement of the integration, so if this is negative they could have taken it out and canceled it with the other negative in front.

For 2:

I'm not quite sure what you mean -- the field can do both positive and negative work, and so can an external force. It just depends on the context.