An electric dipole of dipole moment 2.0 10⁻⁵ C m is initially oriented at an angle of 60^ to a uniform electric field. The external work required to rotate it to an angle of 180^ is 45 mJ. If the magnitude of the electric field is x 10^2 V/m, the value of x is _______.

Step-by-step solution

The work done by an external agent in rotating an electric dipole in a uniform electric field is equal to the change in its potential energy. The potential energy of a dipole is given by U = -pE . The work done is W = U_f - U_i = -pE ₂ - (-pE ₁) = pE( ₁ - ₂) . Given: p = 2.0 10⁻⁵ C m ₁ = 60^ ₂ = 180^ W = 45 mJ = 45 10⁻³ J Substituting the values: W = pE( 60^ - 180^ ) 45 10⁻³ = (2.0 10⁻⁵) E (0.5 - (-1)) 45 10⁻³ = (2.0 10⁻⁵) E 1.5 45 10⁻³ = 3.0 10⁻⁵ E Solving for E : E = 45 10⁻³ 3.0 10⁻⁵ = 15 10^2 V/m. Comparing this