Find the field produced by a uniformly charged sheet carrying 93pC/cm2 .
To find the electric field produced by a uniformly charged sheet, you can use Gauss's law. Gauss's law states that the electric flux through any closed surface is equal to the total charge enclosed by the surface divided by the permittivity of free space (ε₀).
Here are the steps to find the electric field:
1. Start by considering an imaginary Gaussian surface. For a uniformly charged sheet, a convenient choice is a cylinder with one endcap parallel to the sheet and the other endcap perpendicular to it. This allows us to take advantage of the symmetry of the sheet.
2. Determine the charge enclosed by the Gaussian surface. The charge enclosed is the product of the charge density (σ) and the area of the Gaussian cylinder (A).
Charge (Q) = σ × A
Here, the charge density (σ) is given as 93 pC/cm². To convert this to the SI unit of Coulombs/m², divide by 10⁴ as 1 C = 10⁻⁴ C.
σ = (93 × 10⁻¹² C/cm²) ÷ 10⁴ = 9.3 × 10⁻⁸ C/m²
The area of the Gaussian cylinder (A) depends on the specific geometry being considered.
3. Apply Gauss's law to find the electric field.
Gauss's law states: Electric flux (Φ) = Q / ε₀
The electric field (E) is related to the electric flux by: Φ = E × A, where A is the area of the endcap of the Gaussian cylinder perpendicular to the sheet.
Rearranging the equations, we get: E = Q / (ε₀ × A)
4. Substitute the values into the equation.
We can use the value of σ = 9.3 × 10⁻⁸ C/m² we calculated earlier and the known value of the permittivity of free space (ε₀ = 8.854 × 10⁻¹² C²/N·m²).
E = (9.3 × 10⁻⁸ C/m²) / (8.854 × 10⁻¹² C²/N·m² × A)
5. Finally, calculate the electric field (E) by evaluating the expression using the specific dimensions of the Gaussian surface.
Since you haven't provided the dimensions of the sheet, you would need to substitute the appropriate area (A) value based on the dimensions of the Gaussian surface perpendicular to the sheet.
By following these steps, you should be able to calculate the electric field produced by the uniformly charged sheet.