Potential and Energy in Point Charge Fields

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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.