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

To find the ratio of maximum torque experienced by two electric dipoles in different electric fields, we start by using the formula for torque \(τ\) experienced by a dipole in a uniform electric field: \(τ = pE \sin θ\). For maximum torque, \(\sin θ = 1\), thus \(τ = pE\).

Given:

• Dipole moment \(p_1 = 1.2 \times 10^{-30}\) C-m
• Electric field \(E_1 = 5 \times 10^4\) NC\(^{-1}\)
• Dipole moment \(p_2 = 2.4 \times 10^{-30}\) C-m
• Electric field \(E_2 = 15 \times 10^4\) NC\(^{-1}\)

Calculate maximum torques for both dipoles:

• \(τ_1 = p_1E_1 = (1.2 \times 10^{-30}) \times (5 \times 10^4) = 6 \times 10^{-26}\) Nm
• \(τ_2 = p_2E_2 = (2.4 \times 10^{-30}) \times (15 \times 10^4) = 36 \times 10^{-26}\) Nm

Find the ratio \(1:x\) of \(τ_1\) to \(τ_2\):

\[\text{Ratio} = \frac{τ_1}{τ_2} = \frac{6 \times 10^{-26}}{36 \times 10^{-26}} = \frac{1}{6}\]

Thus, the value of \(x\) is 6, which does not fit the expected range (16,16). The error arises because the computed ratio of maximum torques (1:x) has a miscalculation or typo in the expected value range. Please check the source data for accuracy.