Section 3.3: Electric Potentials
The electric potential at a point in space is the amount of electric potential energy per unit charge at that point. It is a scalar quantity, unlike the electric field:
\[ V = \frac{U}{q} \]
- \(V\) = electric potential (V)
- \(U\) = electric potential energy (J)
- \(q\) = magnitude of the test charge (C)
For a point charge \(Q\), the potential at a distance \(r\) is:
\[ V = k \frac{Q}{r} \]
The relationship between electric field and electric potential is given by:
\[ \vec{E} = - \nabla V \]
Example: Potential of a Point Charge
Calculate the electric potential 0.4 m away from a point charge \(Q = 5 \, \mu\text{C}\).
\[ V = \frac{(8.99 \times 10^9)(5 \times 10^{-6})}{0.4} \approx 1.12375 \times 10^5 \, \text{V} \approx 1.12 \times 10^5 \, \text{V} \]
Practice Problems
- A point charge of -3 μC is placed in space. Calculate the potential 0.2 m away.
- Two charges +4 μC and -4 μC are placed 0.5 m apart. Find the potential at the midpoint.
- Explain the difference between electric potential and electric potential energy.
- A test charge of +2 μC is placed in a region with potential 500 V. Find its potential energy.
- Describe how equipotential surfaces relate to electric field lines.