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Electric Charges and Fields — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsElectric Charges and Fields3 Marks
Question
Using Gauss’s law in electrostatics, deduce an expression for electric field intensity due to a uniformly charged infinite plane sheet. If another identical sheet is placed parallel to it, show that there is no electric field in the region between the two sheets.
✓

Answer

By Gauss’s law $ \oint \overrightarrow{E}.\overrightarrow{ds}=\frac{q}{\epsilon_0}$
$\therefore{2{\text{EA}}}=\frac{\sigma{\text{A}}}{{\epsilon_0}}$
$\therefore\text{E}=\frac{\sigma}{2\epsilon_0}\text{ }\text{or}\frac{\sigma}{2\epsilon_0}\text{A}$
Electric field between two identical charged sheets $\because$  Both the sheets have same charge density, their electric fields will be equal and opposite in the region between the two sheets.
Hence the net field is zero. 
Alternate Answer
$\text{E}_1=\frac{\sigma}{2\epsilon_0}$
$\text{E}_2=-\frac{\sigma}{2\epsilon_0}$
Resultant electric field between the plates $ = E_1 + E_2\frac{\sigma}{2\epsilon_0}-\frac{\sigma}{2\epsilon_0}=0$

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