Question

Two point charges \( -4 \, \mu C \) and \( 4 \, \mu C \), constituting an electric dipole, are placed at \( (-9, 0, 0) \, \text{cm \) and \( (9, 0, 0) \, \text{cm} \) in a uniform electric field of strength \( 10^4 \, \text{N/C} \). The work done on the dipole in rotating it from the equilibrium through \( 180^\circ \) is:}

• A. 14.4 mJ
• B. 18.4 mJ
• C. 12.4 mJ
• D. 16.4 mJ

Hint:

The work done in rotating a dipole in an electric field depends on the initial and final angles of the dipole's orientation.

Answer 1

The Correct Option is A

The work done on a dipole in an electric field when rotated through an angle \( \theta \) is given by: \[ W = -pE \cos(\theta_2) + pE \cos(\theta_1), \] where \( p \) is the dipole moment, \( E \) is the electric field strength, and \( \theta_1 = 0^\circ \) and \( \theta_2 = 180^\circ \). The dipole moment \( p \) is given by: \[ p = q \cdot d, \] where \( q = 4 \, \mu C = 4 \times 10^{-6} \, \text{C} \) and \( d = 9 \, \text{cm} = 0.09 \, \text{m} \). Thus: \[ p = 4 \times 10^{-6} \cdot 0.18 = 7.2 \times 10^{-7} \, \text{C} \cdot \text{m}. \] Now, calculate the work done: \[ W = - (7.2 \times 10^{-7} \cdot 10^4) \left( \cos(180^\circ) - \cos(0^\circ) \right) = - (7.2 \times 10^{-7} \cdot 10^4) \left( -1 - 1 \right). \] \[ W = 14.4 \times 10^{-3} = 14.4 \, \text{mJ}. \]