Chapter 17, Problem 5Q

To determine

Can a particle ever move from a region of low electric potential to one of high potential and yet have its electric potential energy decrease?

Answer to Problem 5Q

Solution:

A particle can move from a region of low electric potential to one of high potential and yet have its electric potential energy decrease

Explanation of Solution

We have potential difference between two points, ${\text{V}}_{ba}=V_b-V_a=\frac{P{E}_b-P{E}_a}{q}$, where $PE$ is the potential energy and q is the charge.

Now consider a negative charge is released, it will move towards positive plate. Because of the acceleration of the charge its kinetic energy increases. When kinetic energy increases potential energy decreases. i.e. $P{E}_{b}P{E}_a$ and ${\text{V}}_{ba}=\frac{P{E}_b-P{E}_a}{q}=\frac{-ve}{-ve}=+ve$, so potential difference between 2 points is positive. Which means negative charge moves to a region of higher potential. So, a particle can move from a region of low electric potential to one of high potential and yet have its electric potential energy decrease.