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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 magnitudes 5*10⁴ N/C and 15*10⁴ N/C respectively. The ratio of the maximum torques on the first to the second dipole is 1/x. Find x.

1. 6
2. 3
3. 4
4. 12

Correct answer: 6

Solution

Maximum torque tau_max = pE. For dipole 1: tau1 = (1.2e-30)(5e4). For dipole 2: tau2 = (2.4e-30)(15e4). Ratio tau1/tau2 = (1.2*5)/(2.4*15) = 6/36 = 1/6. Comparing with 1/x gives x = 6.

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