Electric Potential

• Units and Variables

• $V=\frac{U}{{q}_{0}}$
• Change in Potential Energy of the Charge Field System when test charge q0 moves from A to B

$\mathrm{\Delta U}=-{q}_{0}\underset{A}{\overset{B}{\int }}E\cdot \mathrm{ds}$
• Potential Difference between points A and B

$\mathrm{\Delta V}\equiv \frac{\mathrm{\Delta U}}{{q}_{0}}=-\underset{A}{\overset{B}{\int }}E\cdot \mathrm{ds}$
• Electric Potential due to a point charge at any distance r

$V={k}_{e}\frac{q}{r}$
• Potential Energy associated with a pair of point charges

$U={k}_{e}\frac{{q}_{0}{q}_{1}}{{r}_{\mathrm{12}}}$
• x component of an Electric Field

${E}_{x}=-\frac{\mathrm{dV}}{\mathrm{dx}}$
• Electric Potential due to a continuous charge distribution

$V={k}_{e}\int \frac{\mathrm{dq}}{r}$