This question is incomplete, the complete question is;
The electric force due to a uniform external electric field causes a torque of magnitude 20.0 × 10⁻⁹ N⋅m on an electric dipole oriented at 30° from the direction of the external field. The dipole moment of the dipole is 7.5 × 10⁻¹² C⋅m.
What is the magnitude of the external electric field?
If the two particles that make up the dipole are 2.5 mm apart, what is the magnitude of the charge on each particle?
Answer:
- the magnitude of the external electric field is 5333.3 N/C
- the magnitude of the charge on each particle is 3.0 × 10⁻¹² C ≈ 3 nC
Explanation:
Given that;
Torque = 20.0 × 10⁻⁹ N⋅m
dipole moment = 7.5 × 10⁻¹²
∅ = 30°
The moment T of restoring couple is;
T = PEsin∅
E = T/Psin∅
we substitute
E = 20.0 × 10⁻⁹ N⋅m / (7.5 × 10⁻¹²) sin(30°)
E = 20.0 × 10⁻⁹ / 3.75 × 10⁻¹²
E = 5333.3 N/C
Therefore, the magnitude of the external electric field is 5333.3 N/C
The dipole moment is given by the expression;
p = ql
q = p / l
given that l = 2.5 mm = 0.0025 m
we substitute
q = 7.5 × 10⁻¹² / 0.0025
q = 3.0 × 10⁻¹² C ≈ 3 nC
Therefore, the magnitude of the charge on each particle is 3.0 × 10⁻¹² C ≈ 3 nC
