Section 9.2: Electric Potential
Electric potential is the electric potential energy per unit charge at a point in an electric field. It is a scalar quantity that measures how much work is done in moving a charge from a reference point (often infinity) to a specific location.
\( V \) = electric potential (V, volts)
\( U \) = electric potential energy (J)
\( q \) = test charge (C)
\( Q \) = source charge (C)
\( r \) = distance from the source charge (m)
\( k = 8.99 \times 10^9 \, \text{N·m²/C²} \)
Positive charges produce positive potential, and negative charges produce negative potential. Work done by the electric field in moving a positive charge from high to low potential is positive.
Example 1: Potential Due to a Point Charge
A point charge of 4 μC is located at a point. Find the electric potential at a distance of 0.5 m from the charge.
\( V = k \frac{Q}{r} = 8.99 \times 10^9 \frac{4 \times 10^{-6}}{0.5} \approx 71,920 \, \text{V} \)
Example 2: Electric Potential Energy
A 2 μC test charge is placed 0.3 m from a 5 μC point charge. Calculate the electric potential energy of the system.
\( U = q V = q \cdot k \frac{Q}{r} = 2\times10^{-6} \cdot 8.99 \times 10^9 \cdot \frac{5\times10^{-6}}{0.3} \approx 0.299 \, \text{J} \)
Practice Problems
- A 3 μC point charge is located at a point. Calculate the potential 0.2 m away.
- A 1 μC test charge has potential energy 0.05 J in the electric field. Find the potential at its location.
- Two point charges, 2 μC and 3 μC, are 0.4 m apart. Find the potential at the midpoint between them.
- A 5 μC charge is placed in a uniform electric field of 1000 V/m. Find the potential difference after moving 0.2 m along the field.
- Determine the work done in bringing a 2 μC charge from infinity to a point 0.25 m away from a 4 μC charge.