JEE MAIN - Physics (2025 - 22nd January Morning Shift - No. 6)
A line charge of length $\frac{\mathrm{a}^{\prime}}{2}$ is kept at the center of an edge $B C$ of a cube ABCDEFGH having edge length ' $a$ ' as shown in the figure. If the density of line charge is $\lambda \mathrm{C}$ per unit length, then the total electric flux through all the faces of the cube will be ___________ . (Take, $\epsilon_0$ as the free space permittivity)
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Explanation
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$$\phi = {{{q_{enc}}} \over {{\varepsilon _0}}}$$, $${q_{enc}}$$ = enclosed charge
here, we need three other identical cubes to enclose the charge fully.
So, total four cubes enclose the charge
Hence, $${\phi _{cube}} = {\phi \over 4}$$
$$ = {{{q_{enc}}} \over {4{\varepsilon _0}}} = {{\lambda \left( {{a \over 2}} \right)} \over {4{\varepsilon _0}}} \Rightarrow {\phi _{cube}} = {{\lambda a} \over {8{\varepsilon _0}}}$$
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