Question

The Young’s modulus of a quartz piezoelectric crystal is 100 GPa. The uniaxial stress required to change its polarization by 1% is (give absolute value in GPa) .............. (rounded off to nearest integer).

Hint:

- Hooke’s law: $\sigma = E . \epsilon$. - Convert percentage strain to decimal (1% = 0.01). - Quartz has high stiffness, so small strain requires very large stress.

Answer 1

Correct Answer: 1

Step 1: Recall Hooke’s law.
Stress ($\sigma$) and strain ($\epsilon$) are related as: \[ \sigma = E . \epsilon \] where $E$ is Young’s modulus.
Step 2: Interpret the problem statement.
- We are told polarization changes by 1%. - In piezoelectric crystals, polarization change is directly proportional to strain. - Therefore, we treat this as equivalent to a 1% strain. \[ \epsilon = \frac{1}{100} = 0.01 \]
Step 3: Substitute values.
\[ E = 100 \, \text{GPa}, \epsilon = 0.01 \] \[ \sigma = 100 \times 0.01 = 1 \, \text{GPa} \]
Step 4: Interpretation.
A stress of 1 GPa is required to achieve a 1% change in polarization. This shows the high rigidity of quartz: even small strains need very large stresses because of its large modulus. Final Answer: \[ \boxed{1 \, \text{GPa}} \]