Calculate the capacitance of two plates of equal area of $1 \ m^2$ separated by a distance of $1 \ mm$.

In a parallel plate capacitor,the capacity increases if

In a parallel plate capacitor with air between the plates,each plate has an area of $6 \times 10^{-3} \, m^{2}$ and the distance between the plates is $3 \, mm$. Calculate the capacitance of the capacitor. If this capacitor is connected to a $100 \, V$ supply,what is the charge on each plate of the capacitor?

Assertion : The total charge stored in a capacitor is zero.
Reason : The field just outside the capacitor is $\frac{\sigma }{{{\varepsilon _0}}}$. ( $\sigma $ is the charge density).

Find the distance $d$ (in $mm$) between the plates of a parallel plate capacitor with a plate diameter of $40\, mm$,such that its capacitance is equal to the capacitance of a metallic sphere of radius $1\, mm$.

Two charged capacitors have their outer plates fixed and inner plates connected by a spring of force constant $k$. The charge on each capacitor is $q$. Find the extension in the spring at equilibrium.