An electric dipole is formed by two point charges +2 C and -2 C placed at coordinates (0, 2 mm , 0) and (0, -2 mm , 0) respectively. The dipole is placed in a uniform electric field E = 5 10^5 i N C ⁻¹ . If the magnitude of the torque experienced by the dipole is X 10⁻³ N m , the value of X is _____.

Step-by-step solution

The distance between the two charges is 2a = 2 mm - (-2 mm ) = 4 mm = 4 10⁻³ m . The magnitude of the dipole moment is: p = q(2a) = (2 10⁻⁶ C ) (4 10⁻³ m ) = 8 10⁻⁹ C m The dipole moment vector p is directed from the negative charge to the positive charge, which is along the +y -axis ( j ). The electric field E is along the +x -axis ( i ). Thus, the angle between p and E is 90^ . The magnitude of the torque experienced by the dipole is: = pE 90^ = (8 10⁻⁹) (5 10^5) 1 = 40 10⁻⁴ N m = 4 10⁻³ N m Comparing this with X