Consider a uniform electric field `E = 3xx10^(3) hat(i) N//C`. (a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane ? (b) What is the flux through the same square if the normal to its plane makes a `60^(@)` angle with the x-axis ?

Answer

`50 Nm^(2) C^(-1) ; 25 Nm^(2) C^(-1)`

Explanation

Here, `vec(E) = 5xx10^(3) hat(i) NC^(-1)`
`A = (10 cm)^(2) = (10^(-1) m)^(2) = 10^(-2) m^(2)`
When plane is `||` to Y-Z plane, `theta = 0^(@)`
`= 50 Nm^(2) C^(-1)`
When plane makes an angle of `30^(@)` with X-axis,
`theta = 60^(@)`
`:. phi' = EA cos theta = 5xx10^(3) xx10^(-2) cos 60^(@)`
`= 25 Nm^(2) C^(-1)`