Question

A long 1 metre thick dielectric (ϵ = 3 ϵ₀) slab occupying the region 0 < x < 5 is placed perpendicularly in a uniform electric field \({\bar E_0} = 6{\bar a_X}\). The polarization \({\bar P_i} \) inside the dielectric is

1. 4ϵ₀\({\bar a_X}\)
2. 8ϵ0\({\bar a_X}\)
3. 36ϵ0\({\bar a_X}\)
4. Zero

Answer 1

Correct Answer - Option 1 : 4ϵ₀\({\bar a_X}\)

Concept:

D = ϵ₀ E + P        ---(1)

∵ P = polarization

Where \(D = {\epsilon_0}{\epsilon_r}\;\vec E\)      ---(2)

ϵ_r = Relative Permeability

\({\epsilon_0}{\epsilon_r}\;\vec E = {\epsilon_0}\;\vec E + \vec P\)

\(\vec P = {\epsilon_0}\left( {{\epsilon_r} - 1} \right)\;\vec E\)

∵ X_e = ϵ_r – 1 → susceptibility

\(\vec P = {\epsilon_0}{X_e}\;\vec E\)       ---(3)

Calculation:

Given:

  \({E_0} = 6\;\overrightarrow {{a_x}} = 3\;{\epsilon_0} = {\epsilon_r}{\epsilon_0}\;\;So\;\;{\epsilon_r} = 3\)

\(\vec P = {\epsilon_0}\left( {{\epsilon_r} - 1} \right)\vec E\)

= \({\epsilon_0}\left( {3 - 1} \right)\;6\;\overrightarrow {{a_x}} \)

\(\vec P = 12\;{\epsilon_0}\;\overrightarrow {{a_x}} \)      

None of the option matches with the solution.