Question

A capacitor is composed of three parallel conducting plates. All three plates are of same area A. The first pair of plates are kept a distance d₁ apart and the space between them is filled with a medium of a dielectric e₁. The corresponding data for the second pair are d₂&e₂ respectively. What is the surface charge density on the middle plate?

• A. $\varepsilon _ { 0 } \mathrm {~V} \left[ \frac { \varepsilon _ { 1 } } { \mathrm {~d} _ { 1 } } + \frac { \varepsilon _ { 2 } } { \mathrm {~d} _ { 2 } } \right]$
• B. $- \varepsilon _ { 0 } \mathrm {~V} \left[ \frac { \varepsilon _ { 1 } } { \mathrm {~d} _ { 1 } } + \frac { \varepsilon _ { 2 } } { \mathrm {~d} _ { 2 } } \right]$
• C. $2 \varepsilon _ { 0 } \mathrm {~V} \left[ \frac { \varepsilon _ { 1 } } { \mathrm {~d} _ { 1 } } + \frac { \varepsilon _ { 2 } } { \mathrm {~d} _ { 2 } } \right]$
• D. $- 2 \varepsilon _ { 0 } \mathrm {~V} \left[ \frac { \varepsilon _ { 1 } } { \mathrm {~d} _ { 1 } } + \frac { \varepsilon _ { 2 } } { \mathrm {~d} _ { 2 } } \right]$

Answer 1

Answer: (A)

$\varepsilon _ { 0 } \mathrm {~V} \left[ \frac { \varepsilon _ { 1 } } { \mathrm {~d} _ { 1 } } + \frac { \varepsilon _ { 2 } } { \mathrm {~d} _ { 2 } } \right]$

Answer 2

Equivalent circuit

Total charge on 2 & 2' plate

= $\left[ \frac { \varepsilon _ { 1 } \varepsilon _ { 0 } \mathrm {~A} } { \mathrm {~d} _ { 1 } } + \frac { \varepsilon _ { 2 } \varepsilon _ { 0 } \mathrm {~A} } { \mathrm {~d} _ { 2 } } \right] \mathrm { V }$

s = e₀V $\left[ \frac { \varepsilon _ { 1 } } { \mathrm {~d} _ { 1 } } + \frac { \varepsilon _ { 2 } } { \mathrm {~d} _ { 2 } } \right]$