Question

A winding wire which is used to frame a solenoid can bear a maximum 10 A current. If length of solenoid is 80cm and it's cross sectional radius is 3 cm then required length of winding wire is (B=0.2T)

• A. $1.2\times {10}^{2}m$
• B. $4.8\times {10}^{2}m$
• C. $2.4\times {10}^{3}m$
• D. $6\times {10}^{3}m$

Answer 1

The correct option is C $2.4\times {10}^{3}m$

$B=\frac{{\mu }_{0}Ni}{l}$ where $N=$ Total number of turns, $l=$ length of the solenoid
$\Rightarrow 0.2=\frac{4\pi \times {10}^{-7}\times N\times 10}{0.8}\Rightarrow N=\frac{4\times {10}^4}{\pi }$
Since N turns are made from the winding wire so length of the wire $\left(L\right)=2\pi r\times N$
[$2\pi r=$ length of each turns]
$\Rightarrow L=2\pi \times 3\times {10}^{-2}\times \frac{4\times {10}^4}{\pi }=2.4\times {10}^{3}m$