The electric field in a region is given by vector E = (2i+ 4j + 6k) x 10^3 N/C.

Question

The electric field in a region is given by \(\vec{E}=(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) \times 10^{3} \mathrm{~N} / \mathrm{C}\). The flux of the field through a rectangular surface parallel to x-z plane is \(6.0 \ Nm^2C^{-1}\). The area of the surface is _____ \(cm^2\) .

Answer 1

Answer is : 15

\(\phi=\vec{\mathrm{E}} \cdot \vec{\mathrm{A}}=(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) \times 10^{3} \cdot \mathrm{~A} \hat{\mathrm{j}}\)

\( 6=4 \times 10^{3} \mathrm{~A}\)

\( \mathrm{A}=1.5 \times 10^{-3} \mathrm{~m}^{2}\)

\( =15 \mathrm{~cm}^{2}\)