Two electric dipoles of moments $p$ and $27 p$ are placed in opposite direction on a line at a distance of $24 \mathrm{~cm}$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $p$ is

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Aicharya · Accepted Answer

Consider two dipoles are placed at two points $A$ and $B$ in opposite direction. Let $P$ be the null point, where net electric field intensity is found to be zero. $x$ be distance of point from electric dipole at $A$. By using expression of electric field intensity at axial position due to short electric dipole, $\mathbf{E}=\frac{2 k \mathbf{p}}{r^3}$ $E_1$ and $E_2$ be the magnitudes of electric field due to electric dipole $p$ and $27 p$, which are equal and opposite to produce net electric field zero. Therefore, $E_1=E_2$ $\frac{2 k p}{x^3}=\frac{2 k(27 p)}{(24-x)^3} \Rightarrow \frac{1}{x}=\frac{3}{24-x}$ $24-x=3 x \Rightarrow 24=4 x$ $\Rightarrow \quad x=6 \mathrm{~cm}$ from point $A$

Two electric dipoles of moments $p$ and $27 p$ are placed in opposite direction on a line at a distance of…

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