Question

A plane square sheet of charge of side 60 cm has uniform surface charge density. A electron at 1. cm from the centre of the sheet experiences a force of $1.6\times {10}^{-12}N$ directed away from the sheet. The total charge on the plane square sheet is
$({\epsilon }_0=8.854\times {10}^{-12}{C}^2{m}^{-2}{N}^{-1})$

• A. $16.25\mu C$
• B. $-22.15\mu C$
• C. $-44.27\mu C$
• D. $14.27\mu C$
• E. $-63.74\mu C$

Answer 1

Answer: (E)

$-63.74\mu C$

Electron is $1cm$ from the sheet of charges and is far away from the edges of the sheet. Therefore, the sheet looks effectively infinite.

$E=\frac{q_0}{2{ϵ}_{0}A}$ or $F=-eE=-e\left(\frac{q_0}{2{ϵ}_{0}A}\right)$

$\Rightarrow q_0=-\frac{2{ϵ}_{0}AF}{e}=-\frac{2\times 8.854\times {10}^{-12}\times (0.6{)}^2\times 1.6\times {10}^{-12}}{1.6\times {10}^{-19}}=-63.74\times {10}^{-6}C=-63.74\mu C$