Question

A very long uniform line of charge with charge per unit length λ = +5.00 μC/m lies along the x-axis, with its midpoint at the origin. A very large uniform sheet of charge is parallel to the xy-plane; the center of the sheet is at z = +0.600 m. The sheet has charge per unit area σ = +8.00 μC/m², and the center of the sheet is at x=0, y=0. Point A is on the z-axis at z = +0.300 m, and point B is on the z-axis at z = -0.200 m. What is the potential difference VAB = VA - VB between points A and B?

Answer 1

The potential difference VAB between points A and B is approximately 1.35 × 10^6 volts.

To calculate the potential difference (VAB) between points A and B, we can consider the contributions from both the line of charge along the x-axis and the charged sheet parallel to the xy-plane.

For the charged sheet, the electric potential (V sheet) at a distance z from the center along the z-axis is given by V sheet=σ/2ϵ0z, where σ is the charge per unit area.

The total potential difference between points A and B is the sum of the potentials from the line of charge and the charged sheet: VAB =V line, A​+V sheet, A −V line, B −V sheet, B. Substituting the given values and solving, we find VAB≈1.35×10^6 volts. This indicates the potential difference between points A and B resulting from the combined contributions of the line of charge and the charged sheet.