Given an uniform electric field E =2 x 10^3 i N/C, find the flux of this field through a square of side 20 cm, whose plane is parallel to the y-z pane. What would be the flux through the same square, if the plane makes an angle of 30° with the x-axis?
Answers
Answer:
a) The electric flux is " 0 " when " α = 90°.
b) The electric flux is "46.89 "Nm²/C" when "α = 30°".
Explanation:
Data:
Electric field = E = 2×10³i N/C
Side of square = 20 cm =0.2 m
Area of square = A = 0.2×0.2 m² = 0.04 m²
Required:
Electric flux = Ф = ?
Calculation:
CASE (1)
When square is in Y-Z plane and E along X-axis then the angle between E and plane is 0°.
we know that
Ф = E · A = E A Cos(α) where α is angle between E and A
Putting values we get
Ф = (2×10³) (0.04) Cos(0)
since Cos(90) = 1 so
Ф = (2×10³) (0.04) = 80
Therefor the Ф = 80 when α = 0°
CASE (2)
When square making the angle of 30° with X-axis
we know that
Ф = E · A = E A Cos(α) where α is angle between E and A
Putting values we get
Ф = (2×10³) (0.04) Cos(30)
since Cos(30) = 1/√3 so
Ф = (2×10³) (0.04) (1/√3) = 46.88 ≈ 46.89 Nm²/C
Therefor the Ф = 46.89 Nm²/C when α = 30°