Question

A metal plate of surface area $2m^2$ is charged with $\sqrt{8.85}\mu C.$ What is the mechanical force acting on the plate if it is kept in air? $\left[{\epsilon }_0=8.85\times {10}^{-12}{C}^2\right]$

• A. $0.5N$
• B. $0.25N$
• C. $1N$
• D. $1.5N$

Answer 1

The correct option is B $0.25N$

$E=\frac{Q}{A{\epsilon }_0}$

$E=\sqrt{8.85\times {10}^{-6}}$

Mechanical force $=\frac{1}{2}{\epsilon }_0{E}^2\times A$

$=\frac{1}{2}{\epsilon }_0\frac{Q^2\times A}{A^2{\epsilon }_0^2}$

$f=\frac{1}{2}\frac{Q^2}{A{\epsilon }_0}$

$f=\frac{1}{2}\frac{8.85\times {10}^{-6}}{2\times 8.85\times {10}^{-12}}=\frac{1}{4}$

$F\cong 0.25N$