3.13 Conservation of Electric Energy

Conservation of Electric Energy

Conservation of electric energy states that the total electric energy in a closed system remains constant over time, as energy can neither be created nor destroyed, only converted from one form to another. This principle stems from the broader law of conservation of energy and is vital in understanding electric systems.

Key Points:

1. General Principle:

   • Total energy, including electric potential energy, is conserved in a closed system.
   • Electric energy can be transformed into other forms, such as kinetic energy, thermal energy, or electromagnetic radiation.

2. In Electric Circuits:

   • The energy supplied by a power source equals the energy used by the components and the energy stored (e.g., in capacitors).
   • This ensures the design and efficiency of systems like batteries, generators, and transformers.

3. Applications:

   • Electricity generation and distribution.
   • The design of electronic devices.
   • Energy storage systems (e.g., capacitors).

Electric Fields and Work

Work in electric fields refers to the energy required to move a charge within the field. It is linked to changes in electric potential energy.

Key Points:

1. Formula for Work:

   $$W=q\mathrm{\Delta }V$$

   Where:

   • $W$: Work done (in joules, J)
   • $q$: Charge of the particle
   • $\Delta V$: Change in electric potential (in volts, V)

2. Change in Electric Potential Energy:

   • Work is positive if the charge moves to a higher potential.
   • Work is negative if the charge moves to a lower potential.

3. Relation to Forces:

   • Work can also be calculated using $W = Fd$, where $F$ is the electric force and $d$ is the displacement.
   • From Coulomb’s Law, work relates to the change in electric potential energy: $$\mathrm{\Delta }{U}_E=k\frac{q_1{q}_2}{\mathrm{r<span\; class="vlist"\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"><span\; class="msupsub"><span\; class="vlist-s"></span></span></span><span\; class="vlist-s"\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"></span>}}$$

4. Energy Stored:

   • Work done on charges is stored as potential energy in capacitors or within the field itself.

Electric Potential Energy

Electric potential energy ($U$) is the energy a charged particle has due to its position in an electric field.

Key Points:

1. Definition:

   $$U=qV$$

   Where $q$ is the charge, and $V$ is the electric potential.

2. Properties:

   • Measured in joules (J).
   • Scalar quantity.
   • Related to electric potential ($V = \frac{U}{q}$).

3. Energy Conversion:

   • Can convert into other forms, such as kinetic energy, when charges move in the field.

4. Conservation:

   • The total energy (kinetic + potential) in a closed system, including electric potential energy, is conserved.

Review Note:

The conservation of energy principle applies universally, ensuring that all energy transformations in electric systems are predictable and consistent. These concepts underpin the study of electromagnetism and practical applications in technology.