Question

Explain electrostatic potential due to a point charge

Answer 1

Answer:Point charges, such as electrons, are among the fundamental building blocks of matter. Furthermore, spherical charge distributions (like on a metal sphere) create external electric fields exactly like a point charge. The electric potential due to a point charge is, thus, a case we need to consider. 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 \left(W=\phantom{\rule{0.25em}{0ex}}-q\Delta V\right), it can be shown that the electric potential V of a point charge is

V=\frac{\text{kQ}}{r}\phantom{\rule{0.25em}{0ex}}\left(\text{Point Charge}\right),

where k is a constant equal to

9.0×{\text{10}}^{\text{9}}\phantom{\rule{0.25em}{0ex}}\text{N}\phantom{\rule{0.25em}{0ex}}\text{·}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{\text{2}}\text{/}{\text{C}}^{\text{2}}.

Explanation:

Answer 2

Answer:

$\mathtt{ \implies W = - \int _ { \infty } ^ { r } \frac { Q } { 4 \pi e _ { 0 } r ^ { 2 } } d r ^ { \prime } = \frac { Q } { 4 \pi e _ { 0 } ^ { r } } | _ { \infty } ^ { r } = \frac { Q } { 4 \pi e _ { 0 }}}$