Two electric dipoles of dipole moments 3.9 10⁻³⁰ Cm and 5.2 10⁻³⁰ Cm are placed in two different uniform electric fields of strengths 16 10^4 N C⁻¹ and 4 10^4 N C⁻¹ respectively. What is the ratio of maximum torque experienced by the electric dipoles?

Step-by-step solution

The torque experienced by an electric dipole of moment p in a uniform electric field E is given by = pE . The maximum torque _ max occurs when = 90^ , so _ max = pE . For the first dipole, p₁ = 3.9 10⁻³⁰ Cm and E₁ = 16 10^4 N C ⁻¹ . _ max,1 = (3.9 10⁻³⁰) (16 10^4) = 62.4 10⁻²⁶ Nm . For the second dipole, p₂ = 5.2 10⁻³⁰ Cm and E₂ = 4 10^4 N C ⁻¹ . _ max,2 = (5.2 10⁻³⁰) (4 10^4) = 20.8 10⁻²⁶ Nm . The ratio of the maximum torques is _ max,1 _ max,2 = 62.4 10⁻²⁶ 20.8 10⁻²⁶ = 62.4 20.8 = 3 . Therefore, the ratio is 3:1