Question

A solenoid is $1.5m$ long and its inner diameter is $4.0$cm. It has $3$ layers of winding's of $1000$ turns each and carries a current of $2.0$ amperes. The magnetic flux for a cross-section of the solenoid is nearly.

• A. $4.1\times {10}^{-5}$ weber
• B. $5.2\times {10}^{-5}$ weber
• C. $6.31\times {10}^{-3}$ weber
• D. $2.5\times {10}^{-7}$ weber

Answer 1

The correct option is C $6.31\times {10}^{-3}$ weber

Magnetic flux $\left(\varphi \right)=nBA$
Where $n$ is number of turns, B is magnetic field and A is area
Given, $n=1000,i=2$ amp $r=0.02$ and $l=1.5m$
Magnetic field of solenoid of length $l$ is

$B=\frac{{\mu }_{0}i}{l}$

$\varphi =\frac{{\mu }_{0}niA}{l}$

$\varphi =\frac{3\times {10}^{-7}\times 4\pi \times (1000{)}^2\times 2\times \pi (2\times {10}^{-2}{)}^2}{1.5}$

$=6.31\times {10}^{-3}Wb$