Two infinitely long parallel conducting plates having surface . . .

Question : Two infinitely long parallel conducting plates having surface charge densities +ρ and -ρ respectively, are separated by a small distance. The medium between the plates is mica. If ε is the dielectric permittivity of mica, then the electric field E in the region between the plates is

a) less than ρ/ε₀ N/C

b) E=ρ/ε₀ N/C

c) E>ρ/2ε₀ N/C

d) E=ρ/2ε₀ N/C

Doubt by Ananya

Solution : 

We know, electric field between two equal and oppositely charged plates having vacuum between them will be given by 

E₀=ρ/ε₀ — (1)

But when the space between them is filled with a dielectric substance mica then 

E=ρ/Kε₀ 

where K is the dielectric constant of mica. 

E=ρ/Kε₀ OR
E = ρ/ε — (2)

Dividing (2) by (1)

E/E₀=(ρ/ε)/ρ/ε₀ 
E/E₀=ε₀/ε

E/E₀=1/K [∵K=ε/ε₀]
E=E₀/K

Clearly 
E<E₀
E<ρ/ε₀ N/C

Hence, the new electric field in the region between the plates will be less than ρ/ε₀ N/C.

Hence, a) less than ρ/ε₀ N/C will be the correct option.