The electric field on two sides of a large charged plate is shown in figure. The charge density on the plate in SI units is given by

Q. The electric field on two sides of a large charged plate is shown in figure. The charge density on the plate in SI units is given by (ε₀ is the permittivity of free space in SI units)

(a) 2ε₀

(b) 4ε₀

(c) 10ε₀

(d) zero

Ans: (b)

Sol: Let external electric field = E

Charge density = σ

Electric field due to large plate
$ \displaystyle = \frac{\sigma}{2 \epsilon_0} $

$ \displaystyle E – \frac{\sigma}{2 \epsilon_0} = 8 $ …(i)

$ \displaystyle E + \frac{\sigma}{2 \epsilon_0} = 12$ …(ii)

On solving (i) & (ii)

σ = 4ε_o