Section 4.3: Electric Potential Energy
Electric potential energy represents the energy stored due to the position of a charge in an electric field. It is crucial for understanding work done by or against electric forces.
Electric Potential Energy Formula:
- \( U = k \frac{q_1 q_2}{r} \)
- Where \( k = 9 \times 10^9 \, \text{N·m²/C²} \)
- Sign: Positive for like charges (repulsive), negative for opposite charges (attractive).
Relation to Work and Potential Difference:
\( W = -\Delta U \), and \( V = \frac{U}{q} \)
Example 1
Two charges, 2 μC and 3 μC, are 0.5 m apart. Find the electric potential energy of the system.
\( U = k \frac{q_1 q_2}{r} = (9 \times 10^9)(2 \times 10^{-6})(3 \times 10^{-6}) / 0.5 = 0.108 \, \text{J} \)
Example 2
Two opposite charges, -1 μC and 4 μC, are 0.2 m apart. Determine the potential energy.
\( U = (9 \times 10^9)(-1 \times 10^{-6})(4 \times 10^{-6}) / 0.2 = -0.18 \, \text{J} \)
Practice Problems
- Find the electric potential energy between charges 3 μC and 5 μC separated by 0.4 m.
- Two charges -2 μC and 6 μC are 0.3 m apart. Calculate the potential energy.
- A system has charges 1 μC, 2 μC, and 3 μC at the vertices of a triangle. Find total potential energy.
- Charges 2 μC and 2 μC are separated by 0.25 m. Compute the potential energy.
- A particle of charge +1 μC is moved from 0.1 m to 0.2 m from a 4 μC charge. Determine the work done.
- Find potential energy of charges -3 μC and 5 μC at 0.6 m distance.
- Three charges in a line: +2 μC, -1 μC, +3 μC; compute total potential energy of the system.
- Charge of 1 μC placed midway between -2 μC and 2 μC charges 0.5 m apart. Compute total potential energy.
- Find potential energy between 5 μC and 3 μC separated by 0.2 m.
- A charge -2 μC is 0.4 m from +1 μC. Compute electric potential energy.