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 ?

Options

A. `10 NC^(-1) m^(2)`
B. `15 NC^(-1) m^(2)`
C. `20 NC^(-1) m^(2)`
D. `25 NC^(-1) m^(2)`

Answer

B

Explanation

Here, `vec(E) = 3 xx 10^(3) hat(i) N//C`
i.e., field is along +v direction of x-axis.
Surface area, `S = (10 cm)^(2) = 10^(2) cm^(2) - 10^(2) xx 10^(-4) m^(2) = 10^(-2) m^(2)`.
When normal to the plane makes an angle of `60^(@)` with x-axis, then `theta = 60^(@)`
`phi_(E) = ES cos theta = 3 xx 10^(3) xx 10^(-2) cos 60^(@) = 30 xx (1)/(2) = 15 NC^(-1) m^(2)`