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An electric dipole, consisting of two opposite charges of 2 × 10⁻⁶ C each separated by a distance 3 cm is placed in an electric field of 2 × 10⁵ N/C. Torque acting on the dipole is

  1. \( 12 \times 10^{-1} \, \text{Nm} \)
  2. \( 12 \times 10^{-2} \, \text{Nm} \)
  3. \( 12 \times 10^{-3} \, \text{Nm} \)
  4. \( 12 \times 10^{-4} \, \text{Nm} \)

Correct answer: \( 12 \times 10^{-2} \, \text{Nm} \)

Solution

The torque on an electric dipole in a uniform electric field is given by \( \tau = pE \sin\theta \), where \( p = q \cdot d \) is the dipole moment. Here, \( q = 2 \times 10^{-6} \, \text{C} \), \( d = 3 \, \text{cm} = 0.03 \, \text{m} \), and \( E = 2 \times 10^5 \, \text{N/C} \). Assuming \( \sin\theta = 1 \) (maximum torque), \( \tau = (2 \times 10^{-6})(0.03)(2 \times 10^5) = 12 \times 10^{-2} \, \text{Nm} \).

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