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Electric Charges and Fields — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectric Charges and Fields3 Marks
Question
Define electric flux. Write its SI unit.
Using Gauss’s law, deduce an expression for electric field intensity due to an infinitely long straight uniformly charged wire.
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Answer

The electric flux is defined as$\phi_E=\overrightarrow{E}.\overrightarrow{A}={EA}\cos\theta$
Its S.I unit is $(Nm^{2}C^{-1})$ The Gaussian surface is cylindrical and field is radial. At the cylindrical part of the surface, cylindrical part of the surface, $ \overrightarrow{E}$ is normal to the surface at every point and its magnitude is constant (since it depends only on r). By Gauss’s theorem : $ \oint \overrightarrow{E}.{d}\overrightarrow{S}=\frac{q}{\epsilon_0}$$\therefore(2\pi{rl})=\frac{\lambda{l}}{\epsilon_0}$ 
$\text{or}\text{ }\text{ } E=\frac{\lambda}{2\pi\epsilon_0r}$

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