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Byju's Answer

Standard XII

Physics

Permeability

Electric fiel...

Question

Electric field in the given figure is directed along $+ X$ direction and given by $E_{x} = 5 A_{x} + 2 B$ , where $E$ is in $N C^{- 1}$ and $x$ is in metre, $A$ and $B$ are constants with dimensions. Taking $A = 10 N C^{- 1} m^{- 1}$ and $B = 5 N C^{- 1}$ , calculate
(i) The electric flux through the cube.
(ii) Net charge enclosed within the cube.

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Solution

Given $E_{x} = 5 A_{x} + 2 B$
The electric field at face $M$ where $x = 0$ is
$E_{1} = 2 B$
The electric field at face $N$ where $x = 10 c m = 0.10 m$ is
$E_{2} = 5 A \times 0.10 + 2 B = 0.5 A + 2 B$
The electric flux through face $M$ is
$φ_{1} = {\to E}_{1} \cdot {\to S}_{1} = E_{1} S_{1} cos π = - E_{1} S_{1}$
$= - 2 B \times l^{2}$ where $l = 10 c m = 0.01 m$
The electric flux through face $N$
$φ_{2} = {\to E}_{2} \cdot {\to S}_{2} = E_{2} S_{2} cos 0 = (0.5 A + 2 B) l^{2}$
Net electric flux, $φ = φ_{1} + φ_{2}$
$= - 2 B l^{2} + (0.5 A + 2 B) l^{2} = 0.5 A l^{2}$
$= 0.5 \times 10 \times (0.10)^{2} = 5 \times 10^{- 2} V m$ .

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Electric field in the given figure is directed along +X direction and given by Ex=5Ax+2B, where E is in NC−1 and x is in metre, A and B are constants with dimensions. Taking A=10 NC−1m−1 and B=5 NC−1, calculate(i) The electric flux through the cube.(ii) Net charge enclosed within the cube.