10.0Nm²/C
The Electric flux through an area (A) due to a electric field (E) is given by,
ϕ = E A cos θ --------------------(i)
where;
θ is the angle between the electric field and the area.
When θ and A are held constant, equation (i) becomes;
ϕ = k E
ϕ / E = k --------------------(ii)
Where;
k = constant = A cos θ
Equation (ii) can thus be written as;
ϕ₁ / E ₁ = ϕ₂ / E ₂ ------------------(iii)
Where;
ϕ₁ and E ₁ are the initial values of the flux and electric field
ϕ₂ and E ₂ are the final values of the flux and electric field
According to the question;
E ₂ = 2 x E₁
ϕ₁ = 5.0Nm²/C
Substitute E ₂ = 2 x E₁ into equation (iii) as follows;
ϕ₁ / E ₁ = ϕ₂ / (2 x E₁)
ϕ₁ / E ₁ = ϕ₂ / 2E₁
ϕ₁ / ϕ₂ = E₁ / 2E₁
ϕ₁ / ϕ₂ = 1 / 2
ϕ₂ = 2ϕ₁
Substitute ϕ₁ = 5.0Nm²/C into the above equation as follows;
ϕ₂ = 2 x 5.0Nm²/C
ϕ₂ = 10.0Nm²/C
Therefore, the resulting flux is 10.0Nm²/C
