Physics - Magnetism Question with Solution | TestHub

The magnetic field inside a long solenoid is given by:

$B=\frac{{\mu }_{0}NI}{L}$

where $N$ is the total number of turns, $I$ is the current, and $L$ is the length of the solenoid.

The magnetic flux through the cross-section of the solenoid is:

$\Phi =BA=\frac{{\mu }_{0}NIA}{L}$

The magnetic moment of a solenoid is given by:

$M=NIA$

Substituting $M$ into the flux equation, we get:

$\Phi =\frac{{\mu }_{0}M}{L}$

Rearranging to solve for the magnetic moment $M$:

$M=\frac{\Phi L}{{\mu }_0}$

Given values are:
$\Phi =1.57\times 10^{-6}\text{Wb}$
$L=60\text{cm}=0.6\text{m}$
${\mu }_0=4\pi \times 10^{-7}\text{T m/A}=4\times 3.14\times 10^{-7}\text{T m/A}=12.56\times 10^{-7}\text{T m/A}$

Substituting these values into the formula:

$M=\frac{1.57\times 10^{-6}\times 0.6}{12.56\times 10^{-7}}$

$M=\frac{1.57}{12.56}\times 0.6\times 10$

$M=\frac{1}{8}\times 6=\frac{3}{4}=0.75{\text{A m}}^2$

Answer: $0.75{\text{Am}}^2$