Two electric dipoles of dipole moments 1.2 × 10⁻³⁰ Cm and 2.4 × 10⁻³⁰ Cm are placed in two different uniform electric fields of strengths 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 __________.

Solution

Physics sir · 3 steps

Maximum torque is just pE, so multiply moment by field for each dipole and divide.

1. Torque on a dipole. In a uniform field, a dipole feels a torque τ = pE sin θ. It is largest when the dipole is perpendicular to the field (θ = 90°), so τₘₐₓ = pE.
2. Each dipole. First: τ₁ = 1.2 × 10⁻³⁰ × 5 × 10⁴ = 6 × 10⁻²⁶ N m. Second: τ₂ = 2.4 × 10⁻³⁰ × 15 × 10⁴ = 36 × 10⁻²⁶ N m.

   τ₁/τ₂ = p₁E₁/p₂E₂ = (1.2 × 5)/(2.4 × 15) = 6/36 = 1/6

3. So. The ratio is 1/6, so x = 6.

The common slip: 2. Comparing only the dipole moments and forgetting the different fields gives a ratio of 1/2, so x = 2.

The idea to keep. Maximum torque on a dipole is pE, reached when the dipole sits at right angles to the field. When dipoles sit in different fields, both p and E enter the ratio.

Answer from the NTA final answer key. Solution by PrepWiser.