A -2C charge lies at rest. (a) What is the potential difference between point A, which is 1.5m from the charge, and point B, which is 4m from the charge? (b) What would the work on a 4C charge be to move it from A to B?

• A. (a) −6.9×10⁹ V; (b) +2.7×10¹⁰ J
• B. (a) +6.9×10⁹ V; (b) −2.7×10¹⁰ J
• C. (a) −7.5×10⁹ V; (b) +3.0×10¹⁰ J
• D. (a) +7.5×10⁹ V; (b) −3.0×10¹⁰ J
• E. (a) −1.6×10¹⁰ V; (b) +6.4×10¹⁰ J
• F. (a) +1.6×10¹⁰ V; (b) −6.4×10¹⁰ J

Answer: (D)

Verified step by step guidance

1. To find the potential difference between two points A and B due to a point charge, use the formula for electric potential V at a distance r from a point charge Q: V = (k * Q) / r, where k is Coulomb's constant (8.99 × 10^9 N m²/C²).
2. Calculate the potential at point A (V_A) which is 1.5m from the charge: V_A = (8.99 × 10^9 N m²/C² * -2 C) / 1.5 m.
3. Calculate the potential at point B (V_B) which is 4m from the charge: V_B = (8.99 × 10^9 N m²/C² * -2 C) / 4 m.
4. The potential difference ΔV between points A and B is given by ΔV = V_B - V_A. Substitute the values obtained for V_A and V_B to find ΔV.
5. To find the work done on a 4C charge moving from A to B, use the formula W = q * ΔV, where q is the charge being moved (4C). Substitute the value of ΔV from the previous step to find the work done.