Question

A solenoid is to be constructed with a magnetic field of $0.168\text{T}$ at its center. The radius of solenoid is to be $0.01\text{m}$ and the wire carries a current of $2\text{A}$. If the solenoid is $1.4\text{m}$ long, what is the length of wire needed (in $\text{m}$). The length of the wire needed is $x\times 294\text{m}$. Find the value of $x.$

Answer 1

Let $N$ be number of turns of a selenoid
For a solenoid magnetic field induced at centre is
$B={\mu }_{0}ni\Rightarrow B={\mu }_0\frac{N}{l}i$
$\Rightarrow N=\frac{Bl}{{\mu }_{0}i}$
Total length of wire is
$L=N\times 2\pi r=\frac{Bl\times 2\pi r}{{\mu }_{0}i}=\frac{0.168\times 1.4\times 2\pi \times 0.01\times 10}{4\pi \times {10}^{-7}\times 2}=5880\text{m}$
$\therefore 294\times x=5880$
$x=20$