The electric field in a region is given by \( \vec{E} = (6\hat{\imath} + 3\hat{\jmath} + 5\hat{k})\,\mathrm{N/C} \). The electric flux due to this electric field through an area \( 100\,\mathrm{cm^2} \) lying in the X-Y plane is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 5 \times 10^{-2}\,\mathrm{Nm^2/C} \)
The electric flux through a flat area is \( \Phi = \vec{E}\cdot\vec{A} \). An area in the X-Y plane has its area vector along the \( z \)-axis, so \( \vec{A} = A\,\hat{k} \) and only the \( \hat{k} \) component of the field contributes. The \( \hat{\imath} \) and \( \hat{\jmath} \) parts lie in the plane and give no flux.
\( \displaystyle A = 100\,\mathrm{cm^2} = 100\times10^{-4}\,\mathrm{m^2} = 10^{-2}\,\mathrm{m^2} \)
\( \displaystyle \Phi = (5\,\mathrm{N/C})(10^{-2}\,\mathrm{m^2}) = 5\times10^{-2}\,\mathrm{N\,m^2/C} \)