Two point dipoles of dipole moment $p_{1}$ and $p_{2}$ are at a distance $x$ from each other and…

Two point dipoles of dipole moment $p_{1}$ and $p_{2}$ are at a distance $x$ from each other and $\vec{p}_{1} \| \vec{p}_{2}$ The force between the dipoles is:
  1. $\frac{1}{4 \pi \varepsilon_{0}} \frac{4 p_{1} p_{2}}{x^{4}}$
  2. $\frac{1}{4 \pi \varepsilon_{0}} \frac{3 p_{1} p_{2}}{x^{4}}$
  3. $\frac{1}{4 \pi \varepsilon_{0}} \frac{6 p_{1} p_{2}}{x^{4}}$
  4. $\frac{1}{4 \pi \varepsilon_{0}} \frac{8 p_{1} p_{2}}{x^{4}}$

Solution

Given Two parallel dipoles at distance \(x\) Axial electric field of dipole \(\mathrm{P}_1\) \(\mathrm{E}_{\mathrm{P}_1}=\frac{2 * \mathrm{P}_1}{4 \pi \epsilon_0 * \pi^3}\) Force on dipole \(\mathrm{P}_2\) due to electric field of \(\mathrm{P}_1\) $\begin{aligned} & F=P_{2} * \frac{dE}{dx} \\ & =P_{2} * \frac{d}{dx}\left(\frac{2 P_{1}}{4 \pi \epsilon_{0} * x^{3}}\right) \end{aligned}$ On solving \(\mathrm{F}=-\left(\frac{6 \mathrm{P}_1 \mathrm{P}_2}{4 \pi e_0 * \mathrm{~N}^4}\right)\) The correct option is \(3\)

Asked in: JEE Mains - Electrostatics - Test 5

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