Two very large parallel sheets are 5.00 cm apart. Sheet A carries a uniform surface charge dens

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Two very large parallel sheets are 5.00 cm apart. Sheet A...

Two very large parallel sheets are $5.00 \mathrm{~cm}$ apart. Sheet $A$ carries a uniform surface charge density of $-8.80 \mu \mathrm{C} / \mathrm{m}^{2},$ and sheet $B,$ which is to the right of $A,$ carries a uniform charge density of $-11.6 \mu \mathrm{C} / \mathrm{m}^{2} .$ Assume that the sheets are large enough to be treated as infinite. Find the magnitude and direction of the net electric field these sheets produce at a point (a) $4.00 \mathrm{~cm}$ to the right of sheet $A ;$ (b) $4.00 \mathrm{~cm}$ to the left of sheet $A ;$ (c) $4.00 \mathrm{~cm}$ to the right of sheet $B$.

Key Concepts

Gauss’s Law and Electric Fields

Gauss’s Law relates the electric flux through a closed surface to the charge enclosed by that surface. This principle is used to derive the electric field created by symmetric charge distributions, such as an infinite sheet of charge, where the field is uniform and given by E = ?/(2??), with ? representing the surface charge density.

Electric Field of an Infinite Plane

An infinite plane of charge produces a uniform electric field that is independent of the distance from the plane. This property simplifies calculations in problems where the plates can be approximated as infinite, as the field only depends on the magnitude of the surface charge density and not on the specific geometry or distance from the plane.

Superposition Principle

The net electric field generated by multiple charge distributions is the vector sum of the individual fields produced by each charge or charged object. This principle allows one to calculate the overall field in a system with multiple charged surfaces by summing their respective contributions, taking into account both magnitude and direction.

Field Direction Relative to Charge Sign

The direction of the electric field depends on the sign of the charge on the sheet. For a positively charged plane, the field points away from the surface, while for a negatively charged plane, the field points toward the surface. Understanding this is essential for determining the net field’s direction when combining contributions from multiple charged surfaces.

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