[Physics] Electric potential derivation

electric-fields

The definition of electric potential is the work done per unit charge in moving the charge from infinity to that distance.

Now from Coulomb's law $f=\frac{KQ_1Q_2}{r^2}$

So we can now rearrange for the electric field strength.

$\frac{F}{Q_1}=\frac{KQ_2}{r^2}$

The next bt is where my confusion lies. To get the electric potential equation we clearly have to multiply by r to get F x R=W. But is this not the distance away from the charge and so the work done in moving the charge through that distance as opposed to the distance from infinity?

Best Answer

For a constant force, we can obtain the work by multiplying the force by the distance it is applied over.

If we however have a non-constant force, then the work is $W = \int \vec{F} d\vec{s}$.
In your case, this translates to $W = - \int_{\infty}^{r} \frac{KQ_2}{r'^2} dr'={\frac{KQ_2}{r'}}|^r_{\infty}=\frac{KQ_2}{r}$.

So the fact that you obtain the right answer needs to be called chance because you are not calculating your work correctly.

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