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Can someone please explain in detail why this is so? Thanks in advance.

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- Thread starter zerobladex
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- #1

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Can someone please explain in detail why this is so? Thanks in advance.

- #2

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The electrical potential energy (of a unit positive charge, which is how PE is defined here) between two like charges is positive if the charges are positive, and negative if the charges are negative.

Between two opposite charges it can be either positive or negative depending on where you are in the field in relation to the two charges.

The definition of electrical potential energy at a point is in terms of the work done bringing a unit positive charge from infinity to that point.

- #3

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The work expended towards a force field is negative.

With this arbitrary definition we obtain the result you have stated.

So if you have a charge [tex]q_1>0[/tex] at the origin and a charge [tex]q_2<0[/tex] at [tex]r_2[/tex] then the work you must expend on [tex]q_2[/tex] to pull the charge from infinity to [tex]r_2[/tex] is

[tex]W = V(r_2) = - q_2 \, \int \limits_{\infty}^{r_2} \mathrm{d} \vec r ~ \vec E_1(r) = q_1 \,\int \limits_{\infty}^{r_2} \mathrm{d} \vec r ~ \vec \nabla \phi_1(r) = q_1 \Bigl[\phi_1(r_2) - \phi_1(\infty) \Bigr] = q_2 q_1 \frac{1}{4\pi \varepsilon_0 r_2}[/tex]

The fact that [tex]W<0[/tex] (with the above definition of [tex]q_2, q_1[/tex]) shows, that you have to expend the work towards the force field to bring the charge [tex]q_2[/tex] from infinty to [tex]r_2[/tex] (the force between opposite charges is attractive).

That's it! I hope i could help you!?

- #4

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The electrical potential energy (of a unit positive charge, which is how PE is defined here) between two like charges is positive if the charges are positive, and negative if the charges are negative.

I don't agree with you! Compare

- #5

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I don't agree with you! Compareelectric potentialwithelectric potential energy. Because two like charges are always repulsing each other theelectric potential energybetween them is always positive (cause you have to expend work against the force field to get one charge from infinity to any position).

Not if the charges are negative.

Electrical potential refers to the potential energy of a unit POSITIVE charge.

- #6

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[tex]V(r) = E - T ~ \ne ~ q_{+} \, \phi(r) \qquad \mbox{with} ~ q_{+} ~ \mbox{as unit POSITIVE charge}[/tex]

where [tex]T[/tex] is the kinetic energy of the particle and [tex]E[/tex] the total energy.

- #7

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