Obtain the equation for the electric potential energy of a single charge in an external electric field.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The external electric field $\overrightarrow{E}$ and the corresponding external potential $V$ may vary from point to point.
According to the definition of electric potential,$V$ at a point $P$ is the work done in bringing a unit positive charge from infinity to the point $P$. (We assume the potential at infinity to be zero.)
Thus,the work done in bringing a charge $q$ from infinity to the point $P$ in the external field is $W = qV$.
This work is stored in the form of potential energy $U$ of the charge $q$.
$\therefore U = qV$.
If the point $P$ has a position vector $\vec{r}$ relative to the origin,then the potential energy at point $P$ is $U(\vec{r}) = qV(\vec{r})$.
This means the potential energy in an external field is equal to the product of the electric charge and the electric potential at that point in the external field.

Explore More

Similar Questions

The distance between the plates of a capacitor is $1 \ mm$. An electric field of $5 \times 10^5 \ V/m$ is produced between the two plates. What will be the change in the potential energy $(PE)$ of an electron if it is moved from one plate to the other?

Difficult
View Solution

$A$ mass of $1 \ kg$ carrying a charge of $2 \ C$ is accelerated through a potential difference of $1 \ V$. The velocity acquired by it is:

$A$ ball of mass $1 \, g$ and charge $10^{-8} \, C$ moves from point $A$ $(V_A = 600 \, V)$ to point $B$ where the potential is zero. The velocity of the ball at point $B$ is $20 \, cm/s$. Find the velocity of the ball at point $A$ in $cm/s$.

Difficult
View Solution

Two point charges $A = +3 \text{ nC}$ and $B = +1 \text{ nC}$ are placed $5 \text{ cm}$ apart in air. The work done to move charge $B$ towards $A$ by $1 \text{ cm}$ is

Given $q_1 = +2 \times 10^{-8} \ C$ and $q_2 = -0.4 \times 10^{-8} \ C$. When a charge $q_3 = 0.2 \times 10^{-8} \ C$ is moved from $C$ to $D$,what is the change in the potential energy of $q_3$?

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo