There are two thin parallel charged sheets having surface charge density a placed at a small distance apart. Which of the following statements are correct?
(A) If both the sheets are positively charged, then the electric field between them is $σ/ε_0$
(B) If both the sheets are negatively charged, then the electric field between them is $σ/ε_0$
(C) If the left sheet is positively charged and the right sheet is negatively charged the field between them is $σ/ε_0$
(D) If the right sheet is positively charged and the left sheet is negatively charged then the field between them is $σ/ε_0$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (C) and (D) only
For an infinite sheet of charge with surface charge density $\sigma$, the electric field produced is $E = \frac{\sigma}{2\varepsilon_0}$ on each side, directed away from the sheet if $\sigma$ is positive and toward the sheet if $\sigma$ is negative.
(A) If both sheets are positively charged → between them, fields due to both sheets are in opposite directions, so they cancel partially: $E = \frac{\sigma}{2\varepsilon_0} - \frac{\sigma}{2\varepsilon_0} = 0$ ✖ False
(B) If both sheets are negatively charged → same reasoning, fields oppose → net $E=0$ ✖ False
(C) Left sheet positive, right sheet negative → fields between add up (both point from + to −): $E = \frac{\sigma}{2\varepsilon_0} + \frac{\sigma}{2\varepsilon_0} = \frac{\sigma}{\varepsilon_0}$ ✔ True
(D) Right sheet positive, left sheet negative → again, between them field adds (from + to −): $E = \frac{\sigma}{\varepsilon_0}$ ✔ True
Final Answer:
(C) and (D)