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Question:

Given a uniform electric field →E=2×10³ î N/C. Find the flux of this field through a square of side 20 cm, whose plane is parallel to the y-z plane. What would be the flux through the same square, if the plane makes an angle of 30° with the x-axis?

Solution:

→E=2×10³î (N/C)
Flux=→E.→S=EScosθ
When plane is parallel to Y-Z plane then θ=0
Flux =ES=2×10³×(20×10⁻²)²=2×10³×4×10⁻²=80
when plane makes angle 30 degree with X axis then perpendicular to plane makes angle 60 degree to X axis
hence θ=60°
Flux=ES=2×10³×(20×10⁻²)²×cos60°=2×10³×4×10⁻²× 1/2=40