An electric dipole is placed along the $x$ -axis at the origin $O$. A point $\mathrm{P}$ is at a distance of $20 \mathrm{~cm}$ from this origin such that OP makes an angle $\pi / 3$ with the $x$ -axis. If the electric field at P makes an angle $ heta$ with the $x$ -axis, the value of $ heta$…

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An electric dipole is placed along the $x$ -axis at the origin $O$. A point $\mathrm{P}$ is at a distance of $20 \mathrm{~cm}$ from this origin such that OP makes an angle $\pi / 3$ with the $x$ -axis. If the electric field at P makes an angle $	heta$ with the $x$ -axis, the value of $	heta$ would be

Aicharya · Accepted Answer

From figure, $	heta=\frac{\pi}{3}+\alpha$, where $	an \alpha=\frac{\mathrm{E}_{2}}{\mathrm{E}_{1}}=\left(\frac{\mathrm{p} \sin 	heta}{4 \pi \epsilon_{0} \mathrm{r}^{3}}ight)\left(\frac{4 \pi \in_{0} \mathrm{r}^{3}}{2 \mathrm{p} \cos 	heta}ight)=\frac{1}{2} 	an 	heta$ $	an \left(	heta-\frac{\pi}{3}ight)=\frac{1}{2} 	an \frac{\pi}{3}=\frac{\sqrt{3}}{2}$ or $	heta-\frac{\pi}{3}=	an ^{-1}\left(\frac{\sqrt{3}}{2}ight)$ or $\alpha=	an ^{-1}\left(\frac{\sqrt{3}}{2}ight)$ or $	heta=\frac{\pi}{3}+	an ^{-1}\left(\frac{\sqrt{3}}{2}ight)$

An electric dipole is placed along the $x$ -axis at the origin $O$. A point $\mathrm{P}$ is at a distance of…

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