Answer to Question #89835 in Electricity and Magnetism for Shivam Nishad

Question

The electric field in a certain region is given
by E = 100 k . How much flux passes
through an area A if it is a portion of
i) the xy plane,
ii) the xz plane,
iii) the yz plane ?

Answer 1

The normal vectors to the planes are

$$\begin{matrix} \mathrm{i}) & \pm\mathbf{k} \\ \mathrm{ii}) & \pm\mathbf{j} \\ \mathrm{iii}) & \pm\mathbf{i} \\ \end{matrix}$$

and the electric field is

$$\mathbf{E} = 100\mathbf{k}$$

The flux is

$$\Phi = \int_S \mathbf{E} \, d\mathbf{S}$$

where

$$d\mathbf{S} = \mathbf{n}dA$$

$$\mathbf{En} =\bigg\{\begin{matrix} \mathrm{i}) & \pm\mathbf{Ek} = \pm 100\\ \mathrm{ii}) & \pm\mathbf{Ej} = 0\\ \mathrm{iii}) & \pm\mathbf{Ei} = 0 \\ \end{matrix}$$

so the flux is

$$\Phi = \pm100A$$

depends on the direction of the normal vector of the plain.