In arrangement shown, has two non-conducting plane sheets with charge density σ.

Question

In arrangement shown, has two non-conducting plane sheets with charge density \(\sigma\), and a non-conducting sphere with volume charge density \(\rho\).

Choose the correct relation between the magnitude of electric fields at A, B, C and D. Point A is at the middle of two sheets.

(1) \(E_A = E_{B'}\ E_C\neq E_D\)

(2) \(E_A >E_{B'}\ E_C \neq E_D\)

(3) \(E_A > E_{B'} \ E_C = E_D\)

(4) \(E_A \neq E_B, \ E_C= E_D\)

Answer 1

Correct option is : (2) \(E_A >E_{B'}\ E_C \neq E_D\)

\(\Rightarrow|E_A| = \left|+\frac{\sigma}{2\varepsilon_0} - \frac{\sigma}{2\varepsilon _0} - \frac{1}{4\pi \varepsilon _0}\frac{Q}{r_A^2}\right| = \frac{Q}{4\pi \varepsilon_0r_A^2}\)

\(\Rightarrow|E_B| = \left|+\frac{\sigma}{2\varepsilon_0} - \frac{\sigma}{2\varepsilon _0} - \frac{1}{4\pi \varepsilon _0}\frac{Q}{r_B^2}\right| = \frac{Q} {4\pi \varepsilon _0r_B^2}\)

\(|E_A|> |E_B| \) since \(r_a < r_B\)