Question

A solenoid is $1.5m$ long and its inner diamete is $4.0cm$. It has $3$ layers of windings $1000$ turns each and carries a current of $2.0A$ The magnetic flux for a cross-section of th solenoid is nearly

• A. $4.1\times {10}^{-5}Wb$
• B. $5.2\times {10}^{-5}Wb$
• C. $6.31\times {10}^{-31}Wb$
• D. $2.5\times {10}^{-7}Wb$

Answer 1

Answer: (C)

Magnetic flux is a measure of the quantity of magnetism, taking account of the strength and extent of magnetic field.
$\varphi =nBA$
where $n$ is number of turns, $B$ is magnetic field and $A$ is area.
Given, $n=1000,i=2A,r=2\times 10^{-2}m$
$l=1:5m$
Also magnetic field $B$ of a solenoid of length $l$ is
$B=\frac{{\mu }_{0}ni}{l}$
$\therefore \varphi =\frac{{\mu }_0{n}^{2}iA}{l}$
$=\frac{3\times 10^{-7}\times 4\pi \times (1000{)}^2\times 2\times \pi {\left(2\times 10^{-2}\right)}^2}{1.5}$
$\varphi =6.31\times 10^{-3}Wb$