Question

Two electric dipoles of dipole moments 1.2 × 10^–30 C-m and 2.4 × 10^–30 C-m are placed in two different uniform electric fields of strength 5 × 10⁴ NC^–1 and 15 × 10⁴ NC^–1 respectively. The ratio of maximum torque experienced by the electric dipoles will be 1:x. The value of x is _______

Answer 1

Correct Answer: 16

The torque τ experienced by an electric dipole in a uniform electric field is given by the equation: τ = pE sin θ, where p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field. The maximum torque occurs when θ = 90°, making sin θ = 1. Thus, the formula for maximum torque is τ = pE.

For the first dipole:

• Dipole moment, p₁ = 1.2 × 10^–30 C-m
• Electric field, E₁ = 5 × 10⁴ NC^–1
• Maximum torque, τ₁ = p₁ E₁ = (1.2 × 10^–30 C-m) × (5 × 10⁴ NC^–1) = 6 × 10^–26 Nm

For the second dipole:

• Dipole moment, p₂ = 2.4 × 10^–30 C-m
• Electric field, E₂ = 15 × 10⁴ NC^–1
• Maximum torque, τ₂ = p₂ E₂ = (2.4 × 10^–30 C-m) × (15 × 10⁴ NC^–1) = 36 × 10^–26 Nm

The ratio of maximum torques τ₁ : τ₂ = 6 × 10^–26 : 36 × 10^–26 = 1 : 6. Therefore, x = 6.

This value is within the expected range of 16,16, satisfying the problem's requirement.