Question
Explain Electro static potential energy.
✓
Answer
→Electro static potential energy :
→As shown in the fig. electric charge $Q$ is placed on the origin. Electric field created by it is $\vec{E}$.
→In this electric field, a test charge $q$ is to be taken from R to P , against the repulsive force acting on $q$ by Q .
→The repulsive force between electric charges $q$ and $Q$ can act only when both the charges are either positive or negative. Suppose, both the electric charges are positive.
→Here, test charge $q$ is so small that it doesn't disturb electric charge Q .
→Test charge $q$ is to be taken from point R to P , at a very small and constant velocity. This can become possible only when the external force exerted on charge $q$ is equal and opposite to the electric force exerted on charge $q$ by charge Q . Which means,
$\overrightarrow{ F }_e=-\overrightarrow{ F }_{e xt }$
→In this situation, the work done by the external force on $q$ is stored in the form of potential energy.
→If the external force is removed after taking the charge $q$ at point P , the electric force of repulsion takes the charge $q$ away from Q . Charge $q$ gains kinetic energy.
→We can say that the potential energy stored in charge $q$ at point P , is converted into kinetic energy. In this process, the sum of kinetic energy and potential energy remains constant.
→For the sake of ease, the test charge is taken at infinite distance, initially. (Point - R is at infinite distance)
→The work done by the external force in bringing the test charge from infinity to the point P in the given electric field
$W _{\infty \rightarrow P }=\int_{\infty}^{ P } \overrightarrow{ F }_{e x t} \cdot \overrightarrow{d r}$ →Where the direction of $\overrightarrow{d r}$ will be from $\infty$ towards P .
$\therefore W _{\infty \rightarrow P }=-\int_{\infty}^{ P } \overrightarrow{ F }_e \cdot \overrightarrow{d r}\left(\because \overrightarrow{ F }_e=-\overrightarrow{ F }_{\text {ext }}\right)$
→This work is done against the electrostatic repulsion force, which is stored in charge q in the form of potential energy.
→Static electric energy (electro static potential energy) : "The work required to be done against the electric field in bringing a given test charge(q), from infinite distance to the given point in the electric field is called the electric potential energy of that charge at that point."
→As shown in the fig. electric charge $Q$ is placed on the origin. Electric field created by it is $\vec{E}$.
→In this electric field, a test charge $q$ is to be taken from R to P , against the repulsive force acting on $q$ by Q .
→The repulsive force between electric charges $q$ and $Q$ can act only when both the charges are either positive or negative. Suppose, both the electric charges are positive.
→Here, test charge $q$ is so small that it doesn't disturb electric charge Q .
→Test charge $q$ is to be taken from point R to P , at a very small and constant velocity. This can become possible only when the external force exerted on charge $q$ is equal and opposite to the electric force exerted on charge $q$ by charge Q . Which means,
$\overrightarrow{ F }_e=-\overrightarrow{ F }_{e xt }$
→In this situation, the work done by the external force on $q$ is stored in the form of potential energy.
→If the external force is removed after taking the charge $q$ at point P , the electric force of repulsion takes the charge $q$ away from Q . Charge $q$ gains kinetic energy.
→We can say that the potential energy stored in charge $q$ at point P , is converted into kinetic energy. In this process, the sum of kinetic energy and potential energy remains constant.
→For the sake of ease, the test charge is taken at infinite distance, initially. (Point - R is at infinite distance)
→The work done by the external force in bringing the test charge from infinity to the point P in the given electric field
$W _{\infty \rightarrow P }=\int_{\infty}^{ P } \overrightarrow{ F }_{e x t} \cdot \overrightarrow{d r}$ →Where the direction of $\overrightarrow{d r}$ will be from $\infty$ towards P .
$\therefore W _{\infty \rightarrow P }=-\int_{\infty}^{ P } \overrightarrow{ F }_e \cdot \overrightarrow{d r}\left(\because \overrightarrow{ F }_e=-\overrightarrow{ F }_{\text {ext }}\right)$
→This work is done against the electrostatic repulsion force, which is stored in charge q in the form of potential energy.
→Static electric energy (electro static potential energy) : "The work required to be done against the electric field in bringing a given test charge(q), from infinite distance to the given point in the electric field is called the electric potential energy of that charge at that point."
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→(i) A charge moving with constant speed
(ii) Charge undergoing circular motion
(iii) Fixed charge.
(b) Name that part of electromagnetic spectrum with which waves of frequency
(i) $10^{20} Hz$,
(ii) $10^9 Hz$ associated.