Question

A long uniformly charged wire with linear charge density $\lambda ={\epsilon }_{0}C/m$ is placed in the form of a spiral of outer radius $R=1m$ and having a total $N=160$ turns as shown in the figure. A dipole of dipole moment $|\vec{p}|=0.1Cm$ is placed along the $x$-axis at a point $(a,0,0)$, where $a=\sqrt{3}m$. Find the magnitude of force (in $N$ ) experienced by the dipole.

Answer 1

Answer: 1

$R$ length has turn $=N$
$dr$ length has turn $=\frac{N}{dr}$
$dq=\lambda \times 2\pi r\frac{N}{R}dr$
$\frac{dq}{2\pi rdr}=\frac{\lambda N}{R}=$ Constant $=\sigma$
Force $=\left(p\frac{dE}{dr}\right)=\frac{\lambda NpR}{2{\epsilon }_0{\left(R^2+a^2\right)}^{3/2}}$
$F=\frac{{\epsilon }_0\times 160\times 0.1\times 1}{2{\epsilon }_0\times (1+3{)}^{3/2}}=1$