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An electric field line emerges from a positive point charge $q_{1}$ at an angle $α$ as shown in the figure. At what angle will the field line enter the charge $- q_{\underline{2}}$ ?

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$β = {αq}_{1} / q_{2}$

$β = \sin^{- 1} [sinα \sqrt{q_{1} / q_{2}}]$

$β = 2 α \sqrt{q_{1} / q_{2}}$

$β = 2 \sin^{- 1} [\sin (α / 2) \sqrt{q_{1} / q_{2}}]$

answer is D.

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Detailed Solution

The no. of lines originating from q₁ will be same as the no. of lines terminating at -q₂ .

$\frac{q_{1}}{4 {πϵ}_{0}} 2 π (1 - \cos α) = \frac{q_{2}}{4 {πϵ}_{0}} 2 π (1 - \cos β) \Rightarrow β = 2 \sin^{- 1} [\sin (α / 2) \sqrt{q_{1} / q_{2}}]$

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