Question

A large sheet of charge has a uniform charge density of 10 μC/m2 . What is the electric field due to this charge at a point just above the surface of the sheet?

Answer 1

The electric field just above the surface of the uniformly charged sheet with a charge density of
`\(10 \, \mu\text{C/m}^2\)` is approximately
`\(5.65 * 10^5 \, \text{N/C}\).`

The electric field
`(\(E\))` just above the surface of a uniformly charged infinite plane sheet can be found using the formula:

`\[ E = (\sigma)/(2 \varepsilon_0) \]`

where:

-
`\(E\)` is the electric field,

-
`\(\sigma\)` is the charge density on the sheet,

-
`\(\varepsilon_0\)` is the permittivity of free space
`(\(\varepsilon_0 \approx 8.85 * 10^(-12) \, \text{C}^2/\text{N}\cdot\text{m}^2\))`.

Given that the charge density
`(\(\sigma\))` is
`\(10 \, \mu\text{C/m}^2\)`, which can be converted to
`\(10^(-5) \, \text{C/m}^2\),` we can substitute these values into the formula:

`\[ E = (10^(-5))/(2 * 8.85 * 10^(-12)) \]`

`\[ E = (10^(-5))/(1.77 * 10^(-11)) \]`

`\[ E \approx 5.65 * 10^5 \, \text{N/C} \]`.

Therefore, the electric field just above the surface of the sheet is approximately
`\(5.65 * 10^5 \, \text{N/C}\).`

Answer 2

The electric field just above the surface of a large sheet with a uniform charge density of 10 μC/m2 is calculated using Gauss's Law to be 5.65 x 10^5 N/C.

Step-by-step explanation:

The question asks about the electric field generated by a large sheet of charge with a known uniform charge density. The electric field (E) created by a sheet of charge can be calculated using Gauss's Law. For a sheet with charge density σ (sigma), the electric field is given by E = σ / (2ε0), where ε0 is the vacuum permittivity. In this case, the charge density is 10 μC/m2 (microcoulombs per square meter), so we can plug this value into the formula.

The vacuum permittivity ε0 is a known constant (approximately 8.85 x 10-12 C2/N·m2). Consequently, the electric field just above the surface of the sheet is E = (10 x 10-6 C/m2) / (2 x 8.85 x 10-12 C2/N·m2) = 5.65 x 105 N/C, directed away from the sheet if the charge is positive, or towards the sheet if the charge is negative.