Question 256 of 311

An electric dipole is placed on $x-$axis in proximity to a line charge of linear charge density $3.0\times {10}^{-6}C{m}^{-1}.$ Line charge is placed on $z-$axis and positive and negative charge of dipole is at a distance of $10mm$ and $12mm$ from the origin respectively. If total force of $4N$ is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

A$815.1nC$B$8.8\mu C$C$0.485mC$D$4.44\mu C$

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Answer: (D) $4.44\mu C$

$r=10mm,x=2,$
$\left|{\vec{F}}_{q}\right|=\dfrac{2k\lambda }{r}\cdot q$
$\left|{\vec{F}}_{-q}\right|=\dfrac{2k\lambda }{r+x}\cdot q$
$\left|{\vec{F}}_{net}\right|=\dfrac{2k\lambda q\cdot x}{r(r+x)}$
$4=\dfrac{2\times 9\times {10}^{9}\times 3\times {10}^{-6}\times q\times 2mm}{10mm.12mm}$
$\Rightarrow q=4.44\mu C$