The electric field in a region of space is given by, $\overline{E}=E_0\hat{i}+2E_{0 }\hat{j}$  where ${\mathrm{E}}_0=100 \mathrm{N}/\mathrm{C}$ . The flux of this field through a circular surface of radius 0.02m parallel to the Y-Z plane is nearly:

Given Data: $\overline{E}=E_0\hat{i}+2E_0\hat{j}$ where ${\mathrm{E}}_0=100 \mathrm{N}/\mathrm{C}$

Formula Used: $\varphi =\mathrm{E}·\mathrm{ACos}\theta$

Detailed Solution:

Since the surface area of circular surface is parallel to $\mathrm{Y}-\mathrm{Z}$ plane,
y component of electric field will not contribute to the flux through circular surface.

So, $\varphi =\pi r^2{\mathrm{E}}_{\mathrm{o}}=3.14\times 0.0004\times 100=0.125{\mathrm{Nm}}^2/\mathrm{C}$.