Question

Consider a unifrom electric field `vec(E) = 4xx10^(3) hat(i) NC^(-1)` (i) What is the flux of this field thorough a square of side 10cm on a side whose plane is parallel to Y-Z plane ? (ii) What is the flux through the same square if normal to this plane makes an angle of `60^(@)` with the X-axis ?

Answer 1

(i) Here, normal to a plane parallel to Y-Z plane is along X-direction.
So, `Delta vec(S) = 0.10xx0.10 hat(i) = 0.01 hat(i) m^(2)`
Electric flux `phi_(E) = vec(E). Delta vec(S)`
`= 4xx10^(3) hat(i) . 0.01 hat(i)`
`40 Nm^(2) C^(-1)`
(ii) Here, `theta = 60^(@)`
`phi_(E) = E DeltaS cos 60^(@) = 40xx10^(3) xx0.01 xx cos 60^(@)`
`20Nm^(2) C^(-1)`