Question

A solenoid is $1.5\, m$ long and its inner diamete is $4.0 \,cm$. It has $3$ layers of windings $1000$ turns each and carries a current of $2.0 \,A$ 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.
$\phi=n B A$
where $n$ is number of turns, $B$ is magnetic field and $A$ is area.
Given, $n=1000, i=2\,A , r=2 \times 10^{-2} m$
$l=1: 5 \,m$
Also magnetic field $B$ of a solenoid of length $l$ is
$B=\frac{\mu_{0} n i}{l}$
$\therefore \phi=\frac{\mu_{0} n^{2} i A}{l}$
$=\frac{3 \times 10^{-7} \times 4 \pi \times(1000)^{2} \times 2 \times \pi\left(2 \times 10^{-2}\right)^{2}}{1.5}$
$\phi=6.31 \times 10^{-3} Wb$