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Physics · 2024 · 3 marks
CBSE 2024 · Region 5 · Set 1 · Q23
(a) Define the term 'electric flux' and write its dimensions. (b) A plane surface, in shape of a square of side 1 cm is placed in an electric field E…
(a)
Define the term 'electric flux' and write its dimensions.
(b)
A plane surface, in shape of a square of side $\displaystyle 1$ cm is placed in an electric field $\displaystyle \vec{E}=\left(100 \frac{N}{C}\right) \hat{\mathrm{i}}$ such that the unit vector normal to the surface is given by $\displaystyle \hat{\mathrm{n}}=0.8 \hat{\mathrm{i}}+0.6 \hat{\mathrm{k}}$. Find the electric flux through the surface.
Marking-scheme solution
(a)
It is the measure of the total number of electric field lines passing through a surface normally.
OR
Surface integral of electric field over a surface.
$\displaystyle \phi_{E}=\vec{E} \cdot \vec{A}$
$\displaystyle \left[M L^{3} T^{-3} A^{-1}\right]$
(b)
$\displaystyle \phi_{E}=\vec{E} \cdot \vec{A}$
$\displaystyle =(100 \hat{i}) \cdot\left(10^{-4} \hat{n}\right)$
$\displaystyle =(100 \hat{i}) \cdot(0.8 \hat{i}+0.6 \hat{k}) 10^{-4}$
$\displaystyle =8 \times 10^{-3} \mathrm{~Nm}^{2} \mathrm{C}^{-1}$
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