Question

A uniform surface charge density of +9.5 nC/m^2 is distributed over the entire xy plane. What would be the electric flux through a spherical Gaussian surface centered on the origin and having a radius of 4.5 cm? Suppose we now seek to relate this flux to the electric field caused by the plane. The above would be a good Gaussian surface choice because: (Select ell that apply.) the electric field has a constant size everywhere along this surface the electric field makes a constant angle with respect to n of the surface N/A - this would be a terrible surface choice for finding the electric field

Please provide a step by step solution. Thank you so much for your help!

Answer 1

Surface charge density $\sigma$ = 9.5 x10 ^-9 C / m ²

Radius of spherical surface r = 4.5 cm = 4.5 x10 ^-2 m

Surface area A = 4 $\pi$ r ²

= 4(3.1415)(4.5x10 ^-2) ²

= 254.469x10 ^-4 m ²

Charge q = $\sigma$ A

= (9.5 x10 ^-9 )(254.469x10 ^-4)

= 0.2417 x10 ^-9 C

Electric flux = q / $\varepsilon _{0}$

=(0.2417 x10 ^-9)/(8.85x10 ^-12)

= 27.31 Nm ²/C

= 27 Nm ²/C (Three significant figures)

(b).First two options are correct.