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Question

Two large metal sheets having surface charge density $$+\sigma$$ and $$-\sigma$$ are kept parallel to each other at a small separation distance $$d$$. The electric field at any point in the region between the plates is


A
σϵ0
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B
σ2ϵ0
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C
2σϵ0
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D
σ4ϵ0
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Solution

The correct option is A $$\large{\frac{\sigma}{\epsilon_0}}$$

Electric field due to sheet $$A$$, is $${ \vec { E }  }_{ 1 }=\dfrac { \sigma  }{ 2{ \varepsilon  }_{ 0 } } i$$    {in right side of the sheet}
Also, electric field due to sheet $$B$$, is $${ \vec { E }  }_{ 2 }=\dfrac { \sigma  }{ 2{ \varepsilon  }_{ 0 } } i$$    {in left side of the sheet}
$$\therefore $$  Resultant electric field by parallelogram law of vector addition,
$$\vec { E } ={ \vec { E }  }_{ 1 }+{ \vec { E }  }_{ 2 }$$         {$$\because \theta ={ 0 }^{ 0 }$$ between $${ \vec { E }  }_{ 1 }\& { \vec { E }  }_{ 2 }$$}
$$=\dfrac { \sigma  }{ 2{ \varepsilon  }_{ 0 } } +\dfrac { \sigma  }{ 2{ \varepsilon  }_{ 0 } } $$
$$\boxed { \vec { E } =\dfrac { \sigma  }{ { \varepsilon  }_{ 0 } }  } $$

$$\therefore $$  Option (A) is the correct answer.

966429_955940_ans_2db85baa888446b08e812324cbdb8dae.jpg

Physics

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