Question

A 2.0 cm x 3.0 cm rectangle lies in the xy-plane. What is the electric flux through the rectangle if;

𝐸
⃗ 
= (100 
?̂
+ 50 
𝑘
̂
) N/C

Answer 1

Explanations & Calculations

• Area of the rectangle

$\qquad\qquad \begin{aligned} \small a&=\small 2.0\times3.0=6.0cm^2=6\times10^{-4}m^2 \end{aligned}$

• Flux —according to how it's defined— is the amount of field perpendicular to the given area multiplied by that area.
• Now, the field is $\small \vec{E}= 100\hat{i}+50\hat{k}$: given in vector form which makes it even easy to get the answer.
• We need only the perpendicular component of the field and careful observation would give you that, only the component $\small 50$ is perpendicular as it along the k axis which is perpendicular to both $\small X\,\,\,\,and\,\,\,Y$ axes & thus even the $\small XY$ plane.

• Then the flux can be calculated as follows

$\qquad\qquad \begin{aligned} \small \phi &=\small 50NC^{-1}\times 6\times10^{-4}m^2\\&=\small 0.03\,Wb \end{aligned}$

• And if you notice carefully, if the field is given as $\small \vec{E}=100\hat{j}+50\hat{k}$ (as it is not clear enough what is given in the question) would work the same as 50 is again the only component perpendicular.