Consider an electric field `vec(E) = E_(0) hat(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

Here, `vec(E) = E_(0) hat(x)`
In this problem, `hat(x), hat(y)` and `hat(z)` are the unit vectors along x, y and z-axes respectively.
`:.` Shaded area, `vec(A) = vec(PQ) xx vec(PS)`
`vec(A) = (0 hat(x) + a hat(y) + 0 hat(z)) xx (ahat(x) + 0 hat(y) + a hat(z)) = (a^(2) hat(x) - a^(2) hat(z))`
`phi_(epsilon) = vec(E).vec(A) = (E_(0) hat(x)).(a^(2)hat(x) - a^(2) hat(z)) = E_(0) a^(2)`