Electrostatics

JEE Main level, numerical answer, medium

254 of 311

Question 254 of 311

Two electric dipoles of dipole moments 1.2×10−30cm1.2\times {10}^{-30}cm and 2.4×10−30cm2.4\times {10}^{-30}cm are placed in two difference uniform electric fields of strengths 5×104NC−15\times {10}^{4}N{C}^{-1} and 15×104NC−115\times {10}^{4}N{C}^{-1} respectively. The ratio of maximum torque experienced by the electric dipoles will be 1x\dfrac{1}{x}. The value of xx is _____ .

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Answer: 6

Maximum torque experienced by an electric dipole is τmax=PEsin⁡90∘{\tau }_{max}=PE\sin 90^{\circ}.
So, ∣τ∣max⁡=PE{\left|\tau \right|}_{\max }=PE
The ratio is τ1τ2=P1E1P2E2=1.2×10−30×5×1042⋅4×10−30×15×104=16\dfrac{{\tau }_{1}}{{\tau }_{2}}=\dfrac{{P}_{1}{E}_{1}}{{P}_{2}{E}_{2}}=\dfrac{1.2\times {10}^{-30}\times 5\times {10}^{4}}{2\cdot 4\times {10}^{-30}\times 15\times {10}^{4}}=\dfrac{1}{6}

Hence, the value of x=6x=6.

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