Question
Explain the difference between electric potential and electrical potential energy and explain the relationship between them.
✓
Answer
Electric potential is the work done in bringing a unit positive charge from infinity without acceleration, whereas electrical potential energy is the work done in bringing the given charges from infinity to their position
Electric potential,
$V =\frac{1}{4 \pi \in_0}\left(\frac{q_1}{r}\right)$ and $U =\frac{1}{4 \pi \in_0}\left(\frac{q_1 q_2}{r}\right)$
Where symbols have general meanings. It is clear from the above expressions that
$U =\frac{1}{4 \pi \in_0}\left(\frac{q_1}{r}\right)-q_2$
$ U=q_2 . V $
Therefore, the potential energy of a system made up of $q_1$ and $q_2$ charges (which are placed at a distance $r$ from each other) is $U =$ charge $q_2 \times$ (potential at position $q_2$ due to charge $q_1$ ).
Electric potential,
$V =\frac{1}{4 \pi \in_0}\left(\frac{q_1}{r}\right)$ and $U =\frac{1}{4 \pi \in_0}\left(\frac{q_1 q_2}{r}\right)$
Where symbols have general meanings. It is clear from the above expressions that
$U =\frac{1}{4 \pi \in_0}\left(\frac{q_1}{r}\right)-q_2$
$ U=q_2 . V $
Therefore, the potential energy of a system made up of $q_1$ and $q_2$ charges (which are placed at a distance $r$ from each other) is $U =$ charge $q_2 \times$ (potential at position $q_2$ due to charge $q_1$ ).
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