Two point charges q₁ and q₂ (=q₁/2) are placed at points A(0, 1) and B(1, 0) as shown in figur

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1. Electric Charges and Fields

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Two point charges $q_1$ and $q_2 (=q_1/2)$ are placed at points $A(0, 1)$ and $B(1, 0)$ as shown in the figure. The electric field vector at point $P(1, 1)$ makes an angle $\theta $ with the $x-$ axis, then the angle $\theta$ is

A

${\tan ^{ - 1}}\left( {\frac{1}{2}} \right)$

B

${\tan ^{ - 1}}\left( {\frac{1}{4}} \right)$

C

${\tan ^{ - 1}}\left( 1 \right)$

D

${\tan ^{ - 1}}\left( 0 \right)$

Solution

$\mathrm{E}_{\mathrm{A}}=\frac{\mathrm{q}_{1}}{4 \pi \varepsilon_{0}}$

$\mathrm{E}_{\mathrm{B}}=\frac{\mathrm{q}_{1} / 2}{4 \pi \varepsilon_{0}}$

$\tan \theta =\frac{\mathrm{E}_{\mathrm{B}}}{\mathrm{E}_{\mathrm{A}}}=\frac{1}{2} $

$ \theta =\tan ^{-1}\left(\frac{1}{2}\right) $

Standard 12

Physics

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