Question Detail
Question
Three point charges are placed on the x-axis in air: +2.0 µC at x = 20 cm, -3.0 µC at x = 30 cm, and -4.0 µC at x = 40 cm. Find the absolute potential on the axis at x = 0. (Given: k0 = 9.0 × 109 N·m²/C²)
Correct Answer
Option B is the correct answer.
Detailed Explanation
This is Solved Problem 25.9 on page 18. Absolute potential is a scalar quantity, so we sum the contributions from each charge: V = k0 Σ (qi/ri). At x = 0: q1 = +2.0 × 10-6 C, r1 = 0.20 m; q2 = -3.0 × 10-6 C, r2 = 0.30 m; q3 = -4.0 × 10-6 C, r3 = 0.40 m. V = (9.0 × 109) * [(2.0 × 10-6 / 0.20) + (-3.0 × 10-6 / 0.30) + (-4.0 × 10-6 / 0.40)] = (9.0 × 109) * [(10 × 10-6) + (-10 × 10-6) + (-10 × 10-6)] = (9.0 × 109) * (-10 × 10-6) = -90 × 103 V = -90 kV.
Hint
Remember that potential is a scalar quantity, so sum the contributions algebraically, paying close attention to the signs of the charges and converting units (µC to C, cm to m).