Question

Two plates are placed at a separation of 2 cm. An electron placed at the perryferry of one plate reaches the second plate in 2 microsecond. Calculate the inner charge density of the surface assuming the case of infinite plate.

• A. $0.505\times {10}^{-12}C{m}^{-2}$
• B. $0.15\times {10}^{-12}C{m}^{-2}$
• C. $1.01\times {10}^{-12}C{m}^{-2}$
• D. $0.505\times {10}^{-11}C{m}^{-2}$

Answer 1

The correct option is A $0.505\times {10}^{-12}C{m}^{-2}$

Since initial speed is 0.

Using $s=ut+\frac{1}{2}a{t}^2=\frac{1}{2}a{t}^2$

$⟹a=\frac{2s}{t^2}=\frac{2\times 2\times {10}^{-2}}{(2\times {10}^{-6}{)}^2}$

$⟹a={10}^{10}m/s^2$

Now, field between two plates is $E=\frac{\sigma }{{ϵ}_o}$

Force on electron$=F=eE$

And, $F=ma=eE$

$⟹ma=\frac{e\sigma }{{ϵ}_o}$

$⟹\sigma =\frac{ma{ϵ}_o}{e}$

$⟹\sigma =\frac{9.1\times {10}^{-31}\times {10}^{10}\times 8.85\times {10}^{-12}}{1.6\times {10}^{-19}}$

$⟹\sigma =0.505\times {10}^{-12}C/m^2$

Answer-(A)