Question

You’ve hung two very large sheets of plastic facing each other with distance d between them, as shown in FIGURE EX23.19. By rubbing them with wool and silk, you’ve managed to give one sheet a uniform surface charge density $η_{1} = - η_{0}$ and the other a uniform surface charge density $eta sub 2 equals positive 3 eta sub 0$ . What are the electric field vectors at points 1, 2, and 3?

Accepted Answer

Understand the problem: Two large sheets of plastic are facing each other with a distance d between them. Each sheet has a uniform surface charge density: η₁ = -η₀ for one sheet and η₂ = +3η₀ for the other. We need to determine the electric field vectors at three points: 1 (to the left of the sheets), 2 (between the sheets), and 3 (to the right of the sheets). Recall the formula for the electric field due to a uniformly charged infinite sheet: The electric field produced by a single sheet with surface charge density η is given by E = η / (2ε₀), where ε₀ is the permittivity of free space. The direction of the field depends on the sign of the charge: it points away from a positively charged sheet and toward a negatively charged sheet. Analyze the electric field contributions at each point: At point 1 (to the left of both sheets), the field from the negatively charged sheet (η₁ = -η₀) points toward the sheet, while the field from the positively charged sheet (η₂ = +3η₀) points away from it. These fields are in opposite directions, so their magnitudes will subtract. At point 2 (between the sheets), the field from the negatively charged sheet (η₁ = -η₀) points toward the sheet (to the right), and the field from the positively charged sheet (η₂ = +3η₀) also points away from it (to the right). These fields are in the same direction, so their magnitudes will add. At point 3 (to the right of both sheets), the field from the negatively charged sheet (η₁ = -η₀) points toward the sheet (to the left), while the field from the positively charged sheet (η₂ = +3η₀) points away from it (to the right). These fields are in opposite directions, so their magnitudes will subtract. Use the formula E = η / (2ε₀) to calculate the individual contributions and combine them appropriately for each point.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Electric Field

Surface Charge Density

Superposition Principle