Obtain equation of electric energy of a single charge.
Obtain equation of electric energy of a single charge.
The external electric field $\overrightarrow{\mathrm{E}}$ and the corresponding external potential $\mathrm{V}$ may vary from point to point.
According to definition of electric potential $V$ at a point $P$ is the work done in bringing a unit positive charge from infinity to the point $\mathrm{P}$. (We assume the potential at infinity to be zero.) Thus, work done in bringing a charge $q$ from infinity to the point $P$ in the external field is $\mathrm{W}=q \mathrm{~V}$.
This work is stored in the form of potential energy of $q$,
$\therefore \mathrm{U}=q \mathrm{~V}$
If the point $\mathrm{P}$ has position vector $\vec{r}$ relative to origin, then potential energy at point $\mathrm{P}$, $\mathrm{U}(\vec{r})=q \mathrm{~V}(\vec{r})$
Means potential energy in an external field = electric charge $\times$ electric potential in external field.
Similar Questions
Nine point charges are placed on a cube as shown in the figure. The charge $q$ is placed at the body centre whereas all other charges are at the vertices. The electrostatic potential energy of the system will be
Nine point charges are placed on a cube as shown in the figure. The charge $q$ is placed at the body centre whereas all other charges are at the vertices. The electrostatic potential energy of the system will be
If $OP = 1\,\,cm$ and $OS = 2\,\, cm$, work done by electric field in shifting a point charge $\frac {4\sqrt 2}{27}\,\, μC$ from point $P$ to $S$ in given figure is
If $OP = 1\,\,cm$ and $OS = 2\,\, cm$, work done by electric field in shifting a point charge $\frac {4\sqrt 2}{27}\,\, μC$ from point $P$ to $S$ in given figure is
An alpha particle is accelerated through a potential difference of ${10^6}\,volt$. Its kinetic energy will be......$MeV$
An alpha particle is accelerated through a potential difference of ${10^6}\,volt$. Its kinetic energy will be......$MeV$
Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2 - V_1 = 20\ V$. (i.e., plate $2$ is at a higher potential). The plates are separated by $d = 0.1\ m$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1. $ What is its speed when it hits plate $2?$
$(e = 1.6 \times 10^{-19}\ C, m_e= 9.11 \times 10^{-31}\ kg)$
Two insulating plates are both uniformly charged in such a way that the potential difference between them is $V_2 - V_1 = 20\ V$. (i.e., plate $2$ is at a higher potential). The plates are separated by $d = 0.1\ m$ and can be treated as infinitely large. An electron is released from rest on the inner surface of plate $1. $ What is its speed when it hits plate $2?$
$(e = 1.6 \times 10^{-19}\ C, m_e= 9.11 \times 10^{-31}\ kg)$
- [AIEEE 2006]
A point charge $q$ is held at the centre of a circle of radius $r . B, C$ are two points on the circumference of the circle and $A$ is a point outside the circle. If $W_{A B}$ represents work done by electric field in taking a charge $q_0$ from $A$ to $B$ and $W_{A C}$ represents the workdone from $A$ to $C$, then
A point charge $q$ is held at the centre of a circle of radius $r . B, C$ are two points on the circumference of the circle and $A$ is a point outside the circle. If $W_{A B}$ represents work done by electric field in taking a charge $q_0$ from $A$ to $B$ and $W_{A C}$ represents the workdone from $A$ to $C$, then