Question

In a non-uniform electric field given by \[\vec{E} = \alpha x^{1/2} \hat{i}\] with \[\alpha = 800 \text{ N C}^{-1}\text{m}^{-1/2}\], the flux through a cube of side a = 0.1 m oriented with faces perpendicular to the x-axis is approximately:

विकल्प

• 0.75 N m² C⁻¹

• 2.1 N m² C⁻¹

• 1.05 N m² C⁻¹

• 0.5 N m² C⁻¹

Answer 1

For the field \[\vec{E} = \alpha x^{1/2} \hat{i}\], only the two faces perpendicular to the x-axis contribute to flux (E is parallel to dS on these faces). On the left face: \[E_L = \alpha a^{1/2}\], on the right face: \[E_R = \alpha (2a)^{1/2}\]. The net flux is \[\Phi = a^2(E_R - E_L) = \alpha a^{5/2}(\sqrt{2} - 1) \approx 1.05 \text{ N m}^2\text{C}^{-1}\].