Question

An electric dipole is placed on $x$-axis in proximity to a line charge of linear charge density $3.0\times 10^{-6}C/m$. 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. $4.44muC$

Answer 1

Answer: (D)

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