Question

A plane square sheet of charge of side 0.5 m has uniform surface charge density. An 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 (\( \epsilon_0 = 8.854 \times 10^{-12} \text{ C}^2\text{m}^{-2}\text{N}^{-1} \))

• A. \( 16.25 \text{ } \mu\text{C} \)
• B. \( -22.15 \text{ } \mu\text{C} \)
• C. \( -44.27 \text{ } \mu\text{C} \)
• D. \( 144.27 \text{ } \mu\text{C} \)
• E. \( 8.854 \text{ } \mu\text{C} \)

Hint:

For large sheets, the electric field is considered uniform (\(E = \sigma/2\epsilon_0\)) at distances much smaller than the dimensions of the sheet (1 cm vs 50 cm). This makes the field independent of the distance!

Answer 1

The Correct Option is C