Consider an electric field `vecE = E_0hat x`, where `E_0` is a constant. The flux through the shaded area (as shown in the figure) due to this field is

Options

A. `2E_(0)a^(2)`
B. `sqrt(2)E_(0) a^(2)`
C. `E_(0) a^(2)`
D. `(E_(0) a^(2))/(sqrt(2))`

Answer

C

Explanation

Electric flux `phi = E .S ` or ` phi = E S cos theta `
Here `theta` is the angle between E and S .
In this equation `theta = 45^(@)`, because S is perpendicluar ot surface .
`E = E_(0) " "," " S = (sqrt(2a))(a) = sqrt(2)a^(2)`
`therefore phi = (E_(0)) (sqrt(2)a^(2)) cos 45^(@) = E_(0) a^(2) `. Hence , option (C) is correct.