Six infinitely large and thin non-conducting sheets are fixed in configurations I and II. As shown in the figure, the sheets carry uniform surface charge densities which are indicated in terms of σ 0

Question

Six infinitely large and thin non-conducting sheets are fixed in configurations I and II. As shown in the figure, the sheets carry uniform surface charge densities which are indicated in terms of $σ_{0}$ . The separation between any two consecutive sheets is $1 μ m$ . The various regions between the sheets are denoted as $1, 2, 3, 4$ and 5. If $σ_{0} = 9 μ C / m^{2}$ , then which of the following statements is/are correct: (Take permittivity of free space $ϵ_{0} = 9 \times 1 0^{- 12} F / m$ ):

TestHub · Accepted Answer

( E 4 ​ ) I ​ = ( V First ​ ) I ​ ​ 2 ϵ 0 ​ σ 0 ​ ​ [ 1 − 1 + 1 − 1 − 1 + 1 ] = 0 = 2 ϵ 0 ​ − σ 0 ​ ​ [ − 1 + 2 − 3 + 4 − 5 ] d = 2 ϵ 0 ​ − σ 0 ​ ​ [ − 3 ] d = 2 ϵ 0 ​ σ 0 ​ 3 d ​ ​ ​ ( V Last ​ ) I ​ ​ = 2 ϵ 0 ​ − σ 0 ​ ​ [ 1 − 2 + 3 − 4 + 5 ] = 2 ϵ 0 ​ σ 0 ​ ​ [ − 3 d ] ​ ( V First ​ − V Last ​ ) I ​ ​ = ϵ 0 ​ 3 σ 0 ​ d ​ = 9 × 1 0 − 12 3 × 9 × 1 0 − 6 × 1 × 1 0 − 6 ​ = 3 volt ​ ​ ​ ( E 3 ​ ) II ​ = ​ 2 ϵ 0 ​ σ 0 ​ ​ [ 2 1 ​ − 1 + 1 + 1 − 1 + 2 1 ​ ] = 2 ϵ 0 ​ σ 0 ​ ​ = 2 ϵ 0 ​ − σ 0 ​ ​ [ − 1 + 2 − 3 + 4 − 2 5 ​ ] d = 2 ϵ 0 ​ − σ 0 ​ ​ [ 2 − 2.5 ] d = 4 ϵ 0 ​ σ 0 ​ d ​ ​ ( V Last ​ ) II ​ ​ = 2 ϵ 0 ​ − σ 0 ​ ​ [ 1 − 2 + 3 − 4 + 2 5 ​ ] d = 2 ϵ 0 ​ − σ 0 ​ ​ [ 6.5 − 6 ] d = 4 ϵ 0 ​ − σ 0 ​ d ​ ​ ( V First ​ − V Last ​ ) II ​ = 2 ϵ 0 ​ σ 0 ​ d ​  = 0 ​

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