Two electric dipoles of moment P and 64 P are | vedclass

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(A) Let the neutral point $N$ be at a distance $x$ from the dipole of moment $P$ and at a distance $(25 - x)$ from the dipole of moment $64 P$.At the

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$5$

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(A) Let the neutral point $N$ be at a distance $x$ from the dipole of moment $P$ and at a distance $(25 - x)$ from the dipole of moment $64 P$.At the neutral point $N$,the magnitude of the electric field due to dipole $1$ must be equal to the magnitude of the electric field due to dipole $2$.The electric field on the axial line of a dipole is given by $E = \frac{1}{4\pi \varepsilon_0} \cdot \frac{2p}{r^3}$.Equating the fields:$\frac{1}{4\pi \varepsilon_0} \cdot \frac{2P}{x^3} = \frac{1}{4\pi \varepsilon_0} \cdot \frac{2(64P)}{(25 - x)^3}$$\frac{1}{x^3} = \frac{64}{(25 - x)^3}$Taking the cube root on both sides:$\frac{1}{x} = \frac{4}{25 - x}$$25 - x = 4x$$5x = 25$$x = 5 \ cm$.

Two electric dipoles of moment $P$ and $64 P$ are placed in opposite directions on a line at a distance of $25 \ cm$. The electric field will be zero at a point between the dipoles whose distance from the dipole of moment $P$ is.....$cm$.

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