Deriving E = σ/ε for a charged metal plate

[j-lee00]

What is the field near a square metal plate (with infinitesimal thickness)

The answer is E = $$\sigma$$ / $$\epsilon$$

where $$\sigma$$ = Charge per unit area

$$\epsilon$$ = relative permeabily

Please help me to derive this result. using coulombs and then gauss' law

 

[Sourabh N]

What will be the first step?

 

[j-lee00]

For coulomb

$$\int$$ dE = k $$\sigma$$$$\int$$ 1/r^2 dA

Im getting

E = $$\sigma$$ $$\pi$$ / 8 $$\epsilon$$

The symbolys are multiplying not tothe power of. This result is wrong

 

[Sourabh N]

I didn't understand how did u get that answer.
newayz, try using gauss theorem... what is the Gaussian surface here?

 

[j-lee00]

no i want to use colomb

 

[Sourabh N]

K, then you have take a disc with infinitesimal width, find electric field due to it, and integrate for radius = 0 to infinity(coz the sheet is infinite)

 

[j-lee00]

i know

 

[j-lee00]

im just not getting the right ans

 

[Sourabh N]

k, tell me what is electric field at a distance x from the infinitesimally wide disc of radius r ?