Question 247: Electrostatics & Capacitance

Question

A line charge of length $\frac{\mathrm{a}}{2}$ 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)

Accepted Answer

$$\phi  = {{{q_{enc}}} \over {{\varepsilon _0}}}$$, $${q_{enc}}$$ = enclosed charge
here, we need three other identical cubes to enclose the charge fully.
So, total four cubes enclose the charge
Hence, $${\phi _{cube}} = {\phi  \over 4}$$
$$ = {{{q_{enc}}} \over {4{\varepsilon _0}}} = {{\lambda \left( {{a \over 2}} \right)} \over {4{\varepsilon _0}}} \Rightarrow {\phi _{cube}} = {{\lambda a} \over {8{\varepsilon _0}}}$$

Answer

$\frac{\lambda a}{2 \epsilon_0}$

Answer

$\frac{\lambda \mathrm{a}}{8 \epsilon_0}$

Answer

$\frac{\lambda \mathrm{a}}{4 \epsilon_0}$

Answer

$\frac{\lambda \mathrm{a}}{16 \epsilon_0}$

Electrostatics & Capacitance

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