Conisder an electric field `vecE=E_0hatx` where `E_0` is a constant .
The flux through the shaded area (as shown in the figure) due to this field is

Options

A. `2 E_(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)`
Let `hat(x), hat(y)` and `hat(z)` axis respectively.
Refer to figure the shaded area,

`vec(E) = vec(PQ) xx vec(PS)`
`:. vec(A) = (0 hat(x) + a hat(y) + 0 hat(z)) xx (a hat(x) + 0 hat(y) + a hat(z))`
`= (a^(2) hat(x) - a^(2) hat(z))`
Electric flux through the shaded area,
`phi = vec(E). vec(A) = (E_(0) hat(x)). (a^(2) hat(x) - a^(2) hat(z)) = E_(0) a^(2)`