Question

Two square air-filled parallel plates that are initially uncharged are separated by 1.2 mm, and each of them has an area of 190 mm^2. How much charge must be transferred from one plate to the other if 1.1 nJ of energy are to be stored in the plates? ( ε0 = 8.85 × 10^-12 C2/N · m^2)

Answer 1

`5.5\cdot 10^(-11) C`

Step-by-step explanation:

The capacitance of the parallel-plate capacitor is given by:

`C=\epsilon_0 (A)/(d)`

where

`\epsilon_0 = 8.85\cdot 10^(-12) F/m` is the vacuum permittivity

`A=190 mm^2 = 190 \cdot 10^(-6) m^2` is the area of the plates

`d=1.2 mm = 0.0012 m` is the separation between the plates

Substituting,

`C=(8.85\cdot 10^(-12)) (190 \cdot 10^(-6))/(0.0012)=1.4\cdot 10^(-12)F`

The energy stored in the capacitor is given by

`U=(Q^2)/(2C)`

Since we know the energy

`U=1.1 nJ = 1.1 \cdot 10^(-9) J`

we can re-arrange the formula to find the charge, Q:

`Q=√(2UC)=\sqrt{2(1.1\cdot 10^(-9) J)(1.4\cdot 10^(-12)F )}=5.5\cdot 10^(-11) C`