Question

*** Physics 12 Question ***
Electrostatics + Potential energy




Imagine there is a 5.3 x 10^-11 m distance between a proton and an electron. By calculating the potential energy using this formula :
Ep= kq1q2/r

you will get - 4.3 x 10^-18 J

What does the negative sign of potential energy represent? Please explain. Thank you

Answer 1

IN SHORT-> The negative sign represents that 4.3 x 10^-18 J of energy would be released as they attract each other.

IN DETAIL ->>>
These are the two things that play the main role in the actual process

Any system tends to retain ( or attain) the lowest possible energy state.
And ' opposite charges in rest attract each other'


As a proton and an electron are opposite in the sign of their charges ( according to the convention, charge on an electron is taken to be negative of the elementary charge e, and on proton its taken to be positive)

The negative sign here represents that we need to do no external work for these two bodies to come in contact with each other. I.e. the system is in a highly energetic state before hand, and to come to the lowest possible state of energy these two would attract each other and try to decrease the potential energy of the system as much as possible
(since every system wants to become stable).

So, simply speaking the negative sign is nothing but the fact that the system/ structure has enough 'capability'( or potential) to bring together the proton and electron placed the given distance apart, and the energy released during this process would be 4.13 * 10^-18 J in this case..

P.S. All this discussion is based on a closed system and that external parameters have been ignored (as they haven't been mentioned in the question)

Answer 2

And if in case these two were far enough that they cannot influence each other, then they'll have no affect on each other and wouldn't attract each other..
If in case curious, you may solve for a proton and an electron placed a distance 4 centimeter apart.

Answer 3

It's all a convention, but basically the negative sign implies the electron is attracted to the proton