Consider a uniform electric field E = 3 × 103 îN/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?
(a) Electric
field intensity,
= 3 × 103 î N/C
Magnitude
of electric field intensity,
=
3 × 103 N/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
=
= 3 × 103 × 0.01 × cos0°
= 30 N m2/C
(b) Plane makes an angle of 60° with the x-axis. Hence, θ = 60°
Flux,
Φ =
= 3 × 103 × 0.01 × cos60°
= 15 N m2/C