Question

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

• A. $0.485\text{mC}$
• B. $815.1\text{nC}$
• C. $8.8\mu \text{C}$
• D. $4.44\mu \text{C}$

Answer 1

The correct option is D $4.44\mu \text{C}$


$r=10\text{mm},x=2\text{mm}$

Now forces on the charge,

$|\overrightarrow{F_q}|=\frac{2k\lambda }{r}q$

$|\overrightarrow{F_{-q}}|=\frac{2k\lambda }{r+x}q$

$\Rightarrow |\overrightarrow{F_{net}}|=\frac{2k\lambda q}{r}-\frac{2k\lambda q}{r+x}$

$\Rightarrow |\overrightarrow{F_{net}}|=\frac{2k\lambda q.x}{r(r+x)}$

$\Rightarrow 4=\frac{2\times 9\times {10}^9\times 3\times {10}^{-6}\times q\times (2\times {10}^{-3})}{(10\times {10}^{-3})\times (12\times {10}^{-3})}$

$\Rightarrow q=4.44\times {10}^{-6}\text{C}=4.44\mu \text{C}$

Hence, $\left(D\right)$ is the correct answer.