Answer to Question #193002 in Electric Circuits for Samuel

Question #193002

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

𝐸
βƒ— 
= (100 
?Μ‚
+ 50 
π‘˜
Μ‚
) N/C
1
Expert's answer
2021-05-16T17:53:34-0400

Explanations & Calculations


  • Area of the rectangle

a=2.0Γ—3.0=6.0cm2=6Γ—10βˆ’4m2\qquad\qquad \begin{aligned} \small a&=\small 2.0\times3.0=6.0cm^2=6\times10^{-4}m^2 \end{aligned}


  • Flux β€”according to how it's definedβ€” is the amount of field perpendicular to the given area multiplied by that area.
  • Now, the field is Eβƒ—=100i^+50k^\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 50\small 50 is perpendicular as it along the k axis which is perpendicular to both X    and   Y\small X\,\,\,\,and\,\,\,Y axes & thus even the XY\small XY plane.


  • Then the flux can be calculated as follows

Ο•=50NCβˆ’1Γ—6Γ—10βˆ’4m2=0.03 Wb\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 Eβƒ—=100j^+50k^\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.

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