Potential Difference with Calculus Video Lessons

Concept

# Problem: Let A  = (x1, y1) and B = (x2, y2) be two points near and on the same side of a charged sheet with surface charge density+σ. The electric field E due to such a charges sheet has magnitude E = σ/2e0 everywhere, and the field points away from the sheet, as shown in the diagram.Part A. What is the potential difference VAB = VA – VB between points A and B?Part B. If the potential at y = ±∞ is taken to be zero, what is the value of the potential at a point VA at some positive distance y1 from the surface of the sheet?Choices area. ∞b. -∞c. 0d. -E•y1

###### FREE Expert Solution

The potential difference between points A and B can be expressed as:

$\overline{){{\mathbf{V}}}_{\mathbf{A}\mathbf{B}}{\mathbf{=}}{\mathbf{-}}{{\mathbf{\int }}}_{{\mathbf{B}}}^{{\mathbf{A}}}{\mathbf{E}}{\mathbf{·}}{\mathbf{d}}{\mathbf{l}}}$

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###### Problem Details

Let A  = (x1, y1) and B = (x2, y2) be two points near and on the same side of a charged sheet with surface charge density
+σ. The electric field E due to such a charges sheet has magnitude E = σ/2e0 everywhere, and the field points away from the sheet, as shown in the diagram.

Part A. What is the potential difference VAB = VA – VB between points A and B?

Part B. If the potential at y = ±∞ is taken to be zero, what is the value of the potential at a point VA at some positive distance y1 from the surface of the sheet?

Choices are
a. ∞

b. -∞

c. 0

d. -E•y1