Two electric dipoles of moment $\mathrm{P}$ and $27 \mathrm{P}$ are placed on a line with their centres $24…

Two electric dipoles of moment $\mathrm{P}$ and $27 \mathrm{P}$ are placed on a line with their centres $24 \mathrm{~cm}$ apart. Their dipole moments are in opposite direction. At which point the electric field will be zero between the dipoles from the centre of dipole of moment P?
  1. $6 \mathrm{~cm}$
  2. $8 \mathrm{~cm}$
  3. $10 \mathrm{~cm}$
  4. $12 \mathrm{~cm}$

Solution

Dipole of moment $\mathrm{p}$ is at a distance $\mathrm{x}$ from $\mathrm{N}$ At N, $\mid \mathrm{E} . \mathrm{F}$. due to dipole $1|=| \mathrm{E}$. F. due to dipole $2 \mid$ $\begin{aligned} & \therefore \quad \frac{1}{4 \pi \varepsilon_0} \cdot \frac{2 \mathrm{p}}{\mathrm{x}^3}=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{2(27 \mathrm{p})}{(24-\mathrm{x})^3} \\ & \therefore \quad \frac{1}{\mathrm{x}^3}=\frac{27}{(24-\mathrm{x})^3} \Rightarrow \mathrm{x}=6 \mathrm{~cm} . \end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 1)

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