Electric potential

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

  $V=k_e\int \frac{\mathrm{dq}}{r}$