Energy

Electric potential energy

• Electric potential energy is the energy stored in a system of charges due to their positions relative to each other
• $\vec{\mathbf{E}}$ is an uniform electric field,
• $q$ is a tiny positive charge first placed at point $a$ near the positive plate and then released from rest and accelerates toward the negative plate.
  • $W=Fd=qEd$ is the work done by the electric field $E$ to move a charge $q$ a distance $d$
  • $\Delta \mathrm{PE}={\mathrm{PE}}_b-{\mathrm{PE}}_a=-W$ is the change in electric potential energy when a charge $q$ moves from point $a$ to point $b$
• $W_{\text{ext}}=Q_{2}V=k\frac{Q_1{Q}_2}{r}$ is the work done by an external force to move a charge $Q_2$ from infinity to a distance $r$ from a charge $Q_1$
  • $W_{\text{ext}}$ is the work done by an external force (in $\mathsf{J}$)
  • $Q_1$ is the charge creating the electric field (in $\mathsf{C}$)
  • $Q_2$ is the charge being moved (in $\mathsf{C}$)
  • $r$ is the distance between the charges (in $\mathsf{m}$)

Electric energy

• Electric energy is the capacity to do work
• $E={\int }_{t_0}^{t}Pdt={\int }_{t_0}^{t}VIdt$
  • $E$ is electrical energy (in joules) absorbed or supplied by an element from time $t_0$ to time $t$
  • $P$ is power (in watts)
  • $V$ is voltage (in volts)
  • $I$ is current (in amperes)
• Units of electrical energy
  • $1\mathsf{J}=1\mathsf{C}\cdot \mathsf{V}$ (joule)
  • $1\mathsf{kWh}=3.6\times 10^6\mathsf{J}$ (kilowatt-hour) which is the energy consumed by a 1-kilowatt appliance in 1 hour
  • $1\mathsf{eV}=1.6\times 10^{-19}\mathsf{J}$ (electronvolt) which is the energy acquired by a particle carrying a charge whose magnitude equals that on the electron as a result of moving through a potential difference of $1\mathsf{V}$