Answer:
41.4* 10^4 N.m^2/C
Explanation:
given:
E= 4.6 * 10^4 N/C
electric field is 4.6 * 10^4 N/C and square sheet is perpendicular to electric field so, area of vector is parallel to electric field
then electric flux = ∫ E*n dA
= ∫ 4.6 * 10^4 * 3*3
= 41.4* 10^4 N.m^2/C
41.4 x 10⁴ Nm²/C
The electric flux Φ, through a planar area A, is defined as the product of the electric field, the area of the plane and the cosine of the angle θ, between a perpendicular vector to the area and the electric field. i.e
Φ = E A cos θ ----------------(i)
From the question;
E = 4.6 x 10⁴ N/C
A = area of the square = l² [l = length of the square = 3m]
=> A = (3m)² = 9m²
θ = 0° [since the electric field is perpendicular to the square sheet, then the area vector is parallel to the field]
Substitute these values into equation (i) as follows;
Φ = 4.6 x 10⁴ x 9 x cos 0°
Φ = 4.6 x 10⁴ x 9 x 1
Φ = 41.4 x 10⁴ Nm²/C
Therefore, the electric flux through the sheet is 41.4 x 10⁴ Nm²/C
