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 $10 \,mm$ and $12 \,mm$ from the origin respectively. If total force of $4 \,N$ is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

• A. $815.1 \,n C$
• B. $8.8 \,\mu C$
• C. $0.485\, m C$
• D. $4.44\,mu C$

Answer 1

Answer: (D)

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