Question

Two large plane parallel sheets shown in the figure have equal but opposite surface charge densities \(+\sigma\) and \(-\sigma\). A point charge q placed at points \(P_1,P_2,P_3\) experiences forces \(\overrightarrow{F_1},\overrightarrow{F_2},\overrightarrow{F_3}\) respectively. Then,

• A. \(F_1 = 0, F_2 \neq 0, F_3 = 0\)
• B. \(\overrightarrow F_1 = 0, \overrightarrow F_ 2 = 0, \overrightarrow F_3 = 0\)
• C. \(F_1 \neq 0, F_2 \neq 0, F_3 \neq 0\)
• D. \(F_1 = 0, F_3 \neq 0, F_2=0\)

Answer 1

The Correct Option is B

To calculate the forces on a point charge \( q \) at locations \( P_1, P_2, \) and \( P_3 \) situated between two large, parallel plane sheets with equal and opposite surface charge densities \( +\sigma \) and \( -\sigma \), we utilize the superposition principle and the established electric field characteristics of infinite charged sheets. An infinite sheet with charge density \( \sigma \) generates a uniform electric field \( E = \frac{\sigma}{2\varepsilon_0} \) perpendicular to its surface. For two sheets with opposite and equal charges:

• Outside the region between the sheets, the electric fields from each sheet cancel, resulting in a net electric field of \( E = 0 \).
• Inside the region between the sheets, the fields from both sheets add constructively, producing a uniform electric field \( E = \frac{\sigma}{\varepsilon_0} \) directed from the sheet with positive charge density to the sheet with negative charge density.

Position	Electric Field	Force on \( q \)
\( P_1 \) (outside, left of both sheets)	\( E = 0 \)	\( F_1 = qE = 0 \)
\( P_2 \) (between the sheets)	\( E = \frac{\sigma}{\varepsilon_0} \)	\( F_2 = q \cdot \frac{\sigma}{\varepsilon_0} \)
\( P_3 \) (outside, right of both sheets)	\( E = 0 \)	\( F_3 = qE = 0 \)

Therefore, given these conditions for infinite sheets, the forces experienced by the charge are determined to be \(\overrightarrow F_1 = 0\), \(\overrightarrow F_ 2 = 0\), and \(\overrightarrow F_3 = 0\).