Question

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 1

Here, `vec(E) = 3xx10^(3) hat(i) N//C`, i.e., field is along `+` direction of X-axis
Surface area, `s = (10 cm)^(2) = 10^(2) cm^(2) = 10^(2)xx10^(-4) m^(2) = 10^(-2) m^(2)`.
(a) When plane is parallel to yz plane, `theta = 0^(@)`
`phi_(E) = Es cos theta = 3xx10^(3)xx10^(-2) cos 0^(@) = 30 NC^(-1) m^(2)`
(b) When normal to the plate makes an angle of `60^(@)` with X-axis, then `theta = 60^(@)`
`phi_(E) = Es cos theta = 3xx10^(3)xx10^(-2) cos 60^(@) = 30xx (1)/(2) = 15 NC^(-1) m^(2)`