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Chapter 16: Electric Potential

Difficulty Level: At Grade Created by: CK-12
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If there is a strong enough electric field, sparks form in the air where the electricity jumps from one object to another.  In this chapter, we discuss electrical energy and electric potential.

Chapter Outline

Chapter Summary

  1. The electric field between two parallel-plate conductors is considered uniform far away from the plate edges if the size of the plates is large compared to their separation distance.
  2. The potential energy of a charge \begin{align*}q\end{align*} at a point between two parallel-plate conductors is \begin{align*}PE=qEx\end{align*}, a reference point must be given such as \begin{align*}PE=0\end{align*} at \begin{align*}x=0\end{align*}.
  3. A point charge \begin{align*}q\end{align*} has electric potential energy \begin{align*}PE_x\end{align*} and electric potential \begin{align*}V_x\end{align*} at point \begin{align*}x\end{align*}. Thus, \begin{align*}PE_x=qV_x\end{align*}
  4. The word voltage is used when we mean potential difference.
  5. It is common to write \begin{align*}V=Ed\end{align*}, where \begin{align*}V\end{align*} is understood to mean the voltage (or potential difference) between the plates of a parallel-plate conductor and \begin{align*}d\end{align*} is the distance between the plates.
  6. The work done by the electric field in moving a charge between two parallel plate conductors is \begin{align*}W_{field}=-q \Delta V\end{align*}. The work done by an external force is \begin{align*}W_{external \ force}=q \Delta V\end{align*}.
  7. Voltage can be thought of as the work per unit charge \begin{align*}V=\frac{W}{q}\end{align*}; that is, how much work is required per unit charge to move a charged particle in an electric field.
  8. Capacitance of an air-gap capacitor is given by \begin{align*}C = \varepsilon_0 \frac{A}{d}\end{align*} where \begin{align*}A\end{align*} is the area of the capacitor and \begin{align*}d\end{align*} is the separation distance between the plates.
  9. The charge on a capacitor is directly proportional to the voltage of the capacitor \begin{align*}Q = CV\end{align*}.
  10. A dielectric material placed between the plates increases the capacitance of the capacitor. The capacitance of a capacitor with a dielectric is expressed as \begin{align*}C = k\varepsilon_0 \frac{A}{d}\end{align*}, where \begin{align*}k\end{align*} is the dielectric constant.
  11. The energy stored in a capacitor can be expressed as

    \begin{align*}U & = \frac{1}{2}QV\\ U & = \frac{1}{2}QV^2\\ U & = \frac{1}{2} \frac{Q^2}{C}\end{align*}
    Where \begin{align*}Q\end{align*} is the charge on the capacitor and \begin{align*}V\end{align*} is the voltage of the capacitor.

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Difficulty Level:
At Grade
Date Created:
Jan 13, 2016
Last Modified:
Dec 31, 2016
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