An electric dipole of length 2 cm is placed with its axis making an angle of 30º to a uniform electric field 105 N/C. If it experiences a torque of 10 √3 Nm, then the potential energy of dipole will be:
Correct answer: C. -30 J
- A. -10 J
- B. -20 J
- C. -30 J
- D. -40 J
Explanation
The potential energy of a dipole in an electric field is given by the formula U = -pEcosθ, where p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole axis and the electric field. Using the given values: Torque (τ) = pE sinθ = 10√3 Nm. From τ = pE sinθ, we can find the dipole moment (p): p = τ / (E sinθ) = 10√3 / (105 × 0.5) = 2 × 10-4 C·m. Now, use the dipole moment to find the potential energy: U = -pE cosθ = -(2 × 10-4 C·m) × (105 N/C) × (√3/2) = -30 J. Therefore, the correct answer is Option C: -30 J. The other options arise from potential calculation errors, such as misapplying the angle or using incorrect values for the dipole moment.
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