Question

find the electric potential at a distance 'r' from a point charge 'Q'
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Answer 1

$\huge\bigstar\fcolorbox{purple}{aqua}{\tt\pink{AnSwEr}}\bigstar$

Using calculus to find the work needed to move a test charge q from a large distance away to a distance of r from a point charge Q, and noting the connection between work and potential .

$\large\implies\red{(W = −qΔV)}$

★ It can be shown that the electric potential V of a point charge is :-

$\large\implies\green{V= kQr}$

$\huge\dag{\boxed{\blue{V = k Q r}}}$

$\pink{(Point\: Charge)}$

$\mathtt\purple{where\: k\: is\: a\: constant}$

Answer 2

To find :

The electric potential at a distance of ‘r’ from a point charge ‘Q’

Calculation:

Consider the electric potential due to point charge ‘q’. Let A and B be two points at a distance of $r_A$ and $r_B$ from q. As we move from point A to B the change in electric potential is

    $\Delta V_{BA} = V_B-V_A=-\int\limits^{r_B}_{r_A}{E} \, dr$

                                 $=-\int\limits^{r_B}_{r_A}{k\frac{q}{r^2}} \, dr$

                                 $=kq[\frac{1}{r_B} -\frac{1}{r_A} ]$

This will be the change in the potential if we move from point A to B

As with gravitational potential energy, it is more convenient to find electric potential relative to some reference point. Let the reference point be at infinity i.e., $r_A=\infty$

     $V=kq\times\frac{1}{r} = \frac{kq}{r}$

The electric potential at a distance of ‘r’ from a point charge ‘Q’ is  $V=\frac{kq}{r}$