Electrostatics
Intermediate
Electric Potential
Source: High school physics (Chinese)
Problem Sets:
Electrostatics
Problem
Assume the electric potential at infinity is zero. The characteristics of the electric potential U at a point P and the potential energy $E_p$ of a test charge in the electric field of a source charge Q are given in the table below. Complete the table.
| Source Charge | $U_p$ (+ or -) | $E_p$ of +q (+ or -) | $E_p$ of -q (+ or -) | When P moves closer to the source charge |
|---|---|---|---|---|
| Change in U | ||||
| +Q | + | + | Increases | |
| -Q |
Completed Table:
| Source Charge | $U_p$ (+ or -) | $E_p$ of +q (+ or -) | $E_p$ of -q (+ or -) | When P moves closer to the source charge |
|---|---|---|---|---|
| Change in U | ||||
| +Q | + | + | - | Increases |
| -Q | - | - | + | Decreases |
The potential $U$ due to a source charge $Q$ at a distance $r$ is $U = kQ/r$. The potential energy of a test charge $q$ is $E_p = qU$. Moving closer means $r$ decreases. For a source charge $+Q$:
- $U$ is positive. $E_p$ for $+q$ is positive. $E_p$ for $-q$ is negative.
- As $r$ decreases, $U$ increases. $E_p$ for $+q$ increases. $E_p$ for $-q$ decreases. For a source charge $-Q$:
- $U$ is negative. $E_p$ for $+q$ is negative. $E_p$ for $-q$ is positive.
- As $r$ decreases, $U$ becomes more negative (decreases). $E_p$ for $+q$ decreases. $E_p$ for $-q$ increases.