The net electric flux due to a uniform electric field of $3 \times 10^3 \hat{1} \mathrm{NC}^{-1}$ through a…

The net electric flux due to a uniform electric field of $3 \times 10^3 \hat{1} \mathrm{NC}^{-1}$ through a cube of side $20 \mathrm{~cm}$ oriented such that its faces are parallel to the coordinate planes is
  1. $30 \mathrm{Nm}^2 \mathrm{C}^{-1}$
  2. $15 \mathrm{Nm}^2 \mathrm{C}^{-1}$
  3. $0$
  4. $20 \mathrm{Nm}^2 \mathrm{C}^{-1}$

Solution

Uniform electric field, $\mathrm{E}=3 \times 10^3 \hat{\mathrm{i}} \mathrm{N} / \mathrm{C}$ side of cube, $a=20 \mathrm{~cm}=0.20 \mathrm{~m}$ Four face makes the angle between area vector and electric field is $90^{\circ}$. $\phi=(\mathrm{EdA} \cos 90) \times 4=0$ One face makes the angle between area vector and electric field is $0^{\circ}$ $\begin{aligned} & \phi_1=\mathrm{E} \cdot \mathrm{A} \cos 0 \\ & =\mathrm{EA} \end{aligned}$ Other face makes the angle between area vector and electric field is $180^{\circ}$ $\phi_2=\mathrm{EA} \cos 180=-\mathrm{EA}$ The net electric flux is $\begin{aligned} & \phi_{\text {net }}=\phi_1+\phi_2 \\ & =\mathrm{E} A-\mathrm{EA}=0 \end{aligned}$

Asked in: AP EAMCET 2023 (15 May Shift 2)

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