Question

A charge of 87.6 pC is uniformly distributed on the surface of a thin sheet of insulating material that has a total area of 95.2 cm2. A Gaussian surface encloses a portion of the sheet of charge. If the flux through the Gaussian surface is 3.60 N⋅m2/C, what area of the sheet is enclosed by the Gaussian surface?

Answer 1

To find the area of the sheet enclosed by the Gaussian surface, we can use Gauss's law. The enclosed area is approximately 3.66 cm².

Step-by-step explanation:

To find the area of the sheet enclosed by the Gaussian surface, we can use Gauss's law. According to Gauss's law, the flux through a closed surface is equal to the total charge enclosed within the surface divided by the permittivity of vacuum. In this case, the flux is given as 3.60 N⋅m2/C, and the charge enclosed is 87.6 pC.

Using the formula for flux, we can set up the equation as:

Flux = (Charge Enclosed) / (Permittivity of Vacuum) * (Enclosed Area)

Solving for the enclosed area, we get:

Enclosed Area = (Flux * Permittivity of Vacuum) / Charge Enclosed

Plugging in the known values, we have:

Enclosed Area = (3.60 N⋅m2/C * 8.854 × 10-12 C2/N⋅m2) / 87.6 × 10-12 C

Solving this, we find that the area of the sheet enclosed by the Gaussian surface is approximately 3.66 × 10-4 m2, or 3.66 cm2.