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
B
σ2ϵ0
C
2σϵ0
D
σ4ϵ0

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.Physics

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