Electric Potential Energy | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Electric Potential Energy

Potential belongs to a point in a field. Potential energy belongs to a pair of charges at a chosen separation.

Work changes the energy of the charge pair

To push two positive charges closer, an external force must do work against their repulsion. Their potential energy increases.
To separate two opposite charges, an external force must do work against their attraction. Their potential energy also increases towards zero.
The reference value is zero when the separation is infinite.

E_{\mathrm p}=\dfrac{Qq}{4\pi\varepsilon_0r}

Symbols

$E_{\mathrm p}$ = electric potential energy of the charge pair (J)
$Q,q$ = the two point charges (C)
$r$ = separation of the charges (m)

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For two point charges, the sign comes from Qq. Like charges: positive potential energy. Unlike charges: negative potential energy. Both approach zero as separation tends to infinity.

Like charges have a positive product, so their potential energy is positive.
Unlike charges have a negative product, so their potential energy is negative.

Use energy conservation when charges move

Worked example

Two positive charges move apart

Charges of +2.0 nC and +3.0 nC move from 0.10 m apart to 0.20 m apart. Find the change in electric potential energy.

\Delta E_{\mathrm p}=\dfrac{Qq}{4\pi\varepsilon_0}\left(\dfrac{1}{r_2}-\dfrac{1}{r_1}\right)

Qq=6.0\times10^{-18}\ \mathrm{C^2}

\dfrac{1}{r_2}-\dfrac{1}{r_1}=5.0-10

\Delta E_{\mathrm p}=-2.7\times10^{-7}\ \mathrm{J}

Answer

\Delta E_{\mathrm p}=-2.7\times10^{-7}\ \mathrm{J}

The negative change means the potential energy decreases.
If no external work or other energy transfer occurs, kinetic energy increases by the same amount.

Your turnquick check

A positive charge and a negative charge are released from rest. As they move closer, what happens to their electric potential energy and kinetic energy?

Show worked answer

Their negative potential energy becomes more negative, so it decreases. Their kinetic energy increases by the same amount if no other energy transfer occurs.