Let's solve each part step by step: --- ## (a) Electric Potential Difference (\(\Delta V_{AB}\)) **Formula:** The electric potential difference between two points in a uniform electric field \(\vec{E}\) separated by a distance \(d\) is: \[ \Delta V = V_B - V_A = -E \cdot d \] where \(d\) is the distance from A to B, and the negative sign indicates that potential decreases in the direction of the electric field. **Given:** - \(E = 72,000 \ \text{N/C}\) - \(d = .15 \ \text{m}\) - The field points from A to B (A is "upstream," B is "downstream"). **Calculation:** \[ \Delta V_{AB} = V_B - V_A = -E \cdot d \] \[ \Delta V_{AB} = - (72,000 \ \text{N/C}) \times (.15 \ \text{m}) \] \[ \Delta V_{AB} = - 10,800 \ \text{V} \] **Final Answer (a):** \[ \boxed{\Delta V_{AB} = V_B - V_A = -10,800 \ \text{V}} \] --- ## (b) Change in Electric Potential Energy for \(+5.\,\mu\text{C}\) Charge **Formula:** \[ \Delta U = q \Delta V \] **Given:** - \(q = +5.\,\mu\text{C} = 5. \times 10^{-6}\,\text{C}\) - \(\Delta V_{AB} = -10,800\,\text{V}\) **Calculation:** \[ \Delta U = (5. \times 10^{-6}\,\text{C}) \times (-10,800\,\text{V}) \] \[ \Delta U = -.054\,\text{J} \] **Final Answer (b):** \[ \boxed{\Delta U = -.054\,\text{J}} \] --- ## (c) Change in Electric Potential Energy for \(-5.\,\mu\text{C}\) Charge **Given:** - \(q = -5.\,\mu\text{C} = -5. \times 10^{-6}\,\text{C}\) - \(\Delta V_{AB} = -10,800\,\text{V}\) **Calculation:** \[ \Delta U = (-5. \times 10^{-6}\,\text{C}) \times (-10,800\,\text{V}) \] \[ \Delta U = +.054\,\text{J} \] **Final Answer (c):** \[ \boxed{\Delta U = +.054\,\text{J}} \] --- ### **Summary Table** | Subpart | Calculation | Final Answer | |---------|-------------|--------------| | (a) | \(\Delta V_{AB} = -E \cdot d\) | \(\boxed{-10,800 \ \text{V}}\) | | (b) | \(\Delta U = q \Delta V\) | \(\boxed{-.054 \ \text{J}}\) | | (c) | \(\Delta U = q \Delta V\) | \(\boxed{+.054 \ \text{J}}\) | --- **Note:** - "Upstream" is point A (higher potential), "downstream" is point B (lower potential) because electric potential decreases in the direction of the electric field.