Answer :
Answer:
To calculate the torque experienced by an electric dipole in an electric field, we can use the formula:
\[ \tau = p \cdot E \cdot \sin(\theta) \]
Where:
- \( \tau \) is the torque,
- \( p \) is the magnitude of the dipole moment,
- \( E \) is the electric field strength,
- \( \theta \) is the angle between the electric field and the dipole moment.
Given:
- Magnitude of the charges \( q = 2 \mu C = 2 \times 10^{-6} C \),
- Separation between charges \( d = 4 \, \text{cm} = 0.04 \, \text{m} \),
- Electric field strength \( E = 3 \times 10^4 \, \text{V/m} \),
- Angle \( \theta = 30^\circ \).
First, calculate the dipole moment \( p \):
\[ p = q \cdot d \]
\[ p = 2 \times 10^{-6} \, \text{C} \times 0.04 \, \text{m} \]
\[ p = 8 \times 10^{-8} \, \text{C} \cdot \text{m} \]
Now, substitute the given values into the torque formula:
\[ \tau = 8 \times 10^{-8} \, \text{C} \cdot \text{m} \cdot 3 \times 10^4 \, \text{V/m} \cdot \sin(30^\circ) \]
\[ \tau = 8 \times 10^{-8} \, \text{C} \cdot \text{m} \cdot 3 \times 10^4 \, \text{V/m} \cdot 0.5 \]
\[ \tau = 1.2 \times 10^{-2} \, \text{N} \cdot \text{m} \]
So, the torque experienced by the electric dipole is \( 1.2 \times 10^{-2} \, \text{N} \cdot \text{m} \).