Section 4.5: Potential Difference
Potential difference (voltage) between two points is the work done by an external force in moving a unit charge from one point to another against the electric field.
Key Formula:
- Potential Difference: \( V = V_B - V_A = \frac{W_{AB}}{q} \)
- Work done: \( W = q (V_B - V_A) \)
- 1 Volt = 1 Joule per Coulomb
Example 1
A 2 C charge moves through a potential difference of 5 V. Find the work done.
\( W = q \Delta V = 2 * 5 = 10 \text{ J} \)
Example 2
A charge of 0.5 C moves from point A at 12 V to point B at 5 V. Calculate the work done by the electric field.
\( W = q(V_A - V_B) = 0.5 * (12-5) = 0.5 * 7 = 3.5 \text{ J} \)
Practice Problems
- Define potential difference in your own words and give an example.
- A 3 C charge moves through a 10 V potential difference. Calculate the work done.
- A charge of 1.5 C moves from 20 V to 5 V. Find the work done by the field.
- If 12 J of work is done to move 4 C charge, find the potential difference.
- Explain why work done depends on the path in a non-conservative field but not in an electrostatic field.
- Calculate the potential difference between two points 0.2 m apart in a uniform electric field of 50 N/C.
- Explain the relationship between potential difference and kinetic energy change of a charge.
- A charge moves along an equipotential. Determine the work done.
- Explain why potential difference is scalar while electric field is vector.
- Calculate work done if 5 C charge moves through 15 V potential difference.