Consider a uniform electric field E = 3 × 103 î N/C.(a) What is the

1.	Consider a uniform electric field E = 3 × 103 î 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?
Answer» (a) Electric field intensity, E = 3 × 10³ î N/C Magnitude of electric field intensity, \|E\| = 3 × 10³N/C Side of the square, s = 10 cm = 0.1 m Area of the square, A = s² = 0.01 m² The plane of the square is parallel to the y-z plane. Hence, angle between the unit vector normal to the plane and electric field, θ = 0° Flux (ϕ) through the plane is given by the relation, ϕ=\|E\| Acosθ = 3 × 10³ × 0.01 × cos 0° = 30 N m²/C (b) Plane makes an angle of 60° with the x – axis. Hence, θ = 60° Flux,ϕ =\|E\| = 3 × 103 × 0.01 × cos 60° =30×1/2 = 15 N m²/C

Consider a uniform electric field E = 3 × 103 î 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?

Answer»

(a) Electric field intensity, E = 3 × 10³ î N/C
Magnitude of electric field intensity, |E| = 3 × 10³N/C
Side of the square, s = 10 cm = 0.1 m
Area of the square, A = s² = 0.01 m²

The plane of the square is parallel to the y-z plane. Hence, angle between the unit vector normal to the plane and electric field, θ = 0° Flux (ϕ) through the plane is given by the relation,

ϕ=|E| Acosθ
= 3 × 10³ × 0.01 × cos 0°
= 30 N m²/C

(b) Plane makes an angle of 60° with the x – axis. Hence, θ = 60°

Flux,ϕ =|E|
= 3 × 103 × 0.01 × cos 60°

=30×1/2
= 15 N m²/C

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