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Physics · 2024 · 3 marks
CBSE 2024 · Region 1 · Set 1 · Q22
A cube of side 0 · 1 m is placed, as shown in the figure, in a region where electric field E =500 × i exists. Here x is in meters and E in NC^-1.…
A cube of side $\displaystyle 0 \cdot 1 \mathrm{~m}$ is placed, as shown in the figure, in a region where electric field $\displaystyle \overrightarrow{\mathrm{E}}=500 \times \hat{\mathrm{i}}$ exists. Here x is in meters and E in $\displaystyle \mathrm{NC}^{-1}$. Calculate :
(a)
the flux passing through the cube, and
(b)
the charge within the cube.
Marking-scheme solution
Calculating
(a)
\(\displaystyle \varphi_{\mathrm{L}}=\overrightarrow{\mathrm{E}_{\mathrm{L}}} . \vec{A}=-[500 \times 0.1] \times\left[(0.1)^{2}\right]=-0.5 \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-1}\)
\[\varphi_{\mathrm{R}}=\overrightarrow{\mathrm{E}_{\mathrm{R}}} \cdot \vec{A}=[500 \times 0.2] \times\left[(0.1)^{2}\right]=1 \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-1}
\]
Net flux \(\displaystyle =\varphi_{\mathrm{L}}+\varphi_{\mathrm{R}}=0.5 \mathrm{~N} \mathrm{~m}^{2} \mathrm{C}^{-1}\)
(b)
flux, \(\displaystyle \varphi=\frac{\mathrm{q}}{\varepsilon_{\mathrm{o}}}\)
charge, \(\displaystyle \mathrm{q}=\varphi \times \varepsilon_{\mathrm{o}}\)
\[\begin{aligned}
& =0.5 \varepsilon_{\mathrm{o}} \\
& =4.4 \times 10^{-12} \mathrm{C}
\end{aligned}
\]
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