Question

In the given figure a capacitor of plate area $A$ is charged upto a charge $q$. The mass of each plate is $m_2$. The lower plate is rigidly fixed. The value of $m_1$, if the system remains in equilibrium, is

• A. $2m_2+\frac{2q^2}{{ϵ}_{0}Ag}$
• B. $m_2$
• C. $\frac{q^2}{{ϵ}_{0}Ag}+m_2$
• D. $2m_2$

Answer 1

Answer: (C)

$\frac{q^2}{{ϵ}_{0}Ag}+m_2$

FBD on $m_1$

$T=m_{1}g$
we know tension in a string remains same.
$\therefore$ FBD on capacitor plate.
$T=Eq+m_{2}g$
$m_{1}g=\left(\frac{\sigma }{{\epsilon }_0}q\right)+m_{2}g$

$m_1=\frac{q^2}{{\epsilon }_{0}Ag}+m_2$