Question

A quartz crystal has the dimensions of $2mm\times 2mm\times 1mm$. Quartz has the following properties.

$\text{Charge sensitivity = 2pC/N}$
$\text{Young's modulus =}8.6\times {10}^{10}N/m^2$
$\text{Permittivity =}40.6\times {10}^{-12}\left(F/m\right)$

The value of force & charge if the crystal is subjected to a strain of $10\times {10}^{-6}\left(m/m\right)$ is

• A. 3.44N, 6.88 pC
• B. 3N, 6 pC
• C. 6.88N, 3.44pC
• D. 5N, 4.88 pC

Answer 1

The correct option is A 3.44N, 6.88 pC

$Y=\frac{\text{Stress}}{\text{Strain}}$

$\text{Stress}=Y\epsilon =8.6\times {10}^{10}\times 10\times {10}^{-6}$

$S=86\times {10}^{4}N/m^2$

$S=\frac{F}{A}$

$F=SA=86\times {10}^4\times 2\times 2\times {10}^{-6}$

$F=3.44N$

$\text{Charge}=Q=d.F=2\times {10}^{-12}\times 3.44=6.88pC$