Section 3.9: Energy Conservation
In electrostatics, the principle of energy conservation states that the total mechanical energy of a charged particle in an electric field is conserved if only electrostatic forces act.
Conservation Statement:
\[ K_1 + U_1 = K_2 + U_2 \]
where \( K \) is kinetic energy and \( U \) is electric potential energy.
Example 1
A proton is released from rest at a point with potential \( V = 200 \, \text{V} \). Find its speed at \( V = 0 \, \text{V} \).
\[ \Delta V = V_2 - V_1 = 0 - 200 = -200 \, \text{V} \]
\[ \Delta U = q\,\Delta V = (1.6\times10^{-19})(-200) = -3.2\times10^{-17}\, \text{J} \]
\[ K = -\Delta U = 3.2\times10^{-17}\, \text{J} \]
\[ v = \sqrt{\frac{2K}{m_p}} = \sqrt{\frac{2(3.2\times10^{-17})}{1.67\times10^{-27}}} \approx 1.96\times10^5 \, \text{m/s} \]
Practice Problems
- State the principle of conservation of energy in electrostatics.
- A proton is accelerated from rest through 500 V. Find its speed.
- Explain potential and kinetic energy exchange while total energy remains constant.
- List assumptions required for energy conservation in an electric field.
- Relate this principle to conservative forces in mechanics.