Given a uniform electric field `vecE=5xx10^(3)hatiN//C`, find the flux of this field through a square of 10cm on a side whose plane is parallel to the y - z plane. What would be the flux through the same square if the plane makes a `30^(@)` angle with the x-axis?

Explanation

Here, `vecE=5xx10^3hati` N/C, i.e. field is along positive direction of x-axis.
Surface area ,A = 10 cm × 10 cm
= 0.10 m × 0.10 m
`=10^(-2) m^2`
(i) When plane parallel to y – z plane, the normal to plane is along x axis. Hence
`theta=0^@`
`phi=EA cos`
`theta=5xx10^3xx10^(-2)cos 0^@`
`=50 NC^(-1)m^2`
(ii) When the plane makes a `30^@` angle with the x-axis, the normal to its plane makes `60^@` angle with x-axis. Hence
`theta=60^@`
`phi=EAcostheta`
`=5xx10^3xx10^(-2)cos 60^@`
`=25NC^(-1)m^2`