Question

The solenoid has a core with a material of relative permeability of $500$. The windings of the solenoid are insulated from the core and carry a current of $1\text{A}$. If the number of turns is $500$ per meter, then magnetisation is?

• A. $2.5\times {10}^3\text{A/m}$
• B. $2.5\times {10}^5\text{A/m}$
• C. $2.0\times {10}^3\text{A/m}$
• D. $2.0\times {10}^5\text{A/m}$

Answer 1

The correct option is B

$2.5\times {10}^5\text{A/m}$

Step 1: Given

Relative permeability of solenoid's core, ${\mu }_r=500$.
Current in the solenoid, $I=1\text{A}$.
Number of turns in the solenoid, $500{\text{m}}^{-1}$

Step 2: Formulas used

Magnetic intensity,
$H=nI$

Magnetisation,
$M=\chi H$
where $\chi$ is the magnetic susceptibility of the material.

The relationship between relative permeability and magnetic susceptibility is,
$\begin{array}{cc}& {\mu }_r=\chi +1\\ \Rightarrow & \chi ={\mu }_r-1\end{array}$

Step 3: Calculate Magnetic intensity

Magnetic intensity is,
$\begin{array}{rcl}H& =& n·I\\ & =& 500\times 1\\ & =& 500{\text{Am}}^{-1}\end{array}$

So, magnetic intensity, $H=500\text{A/m}$.

Step 4: Calculate magnetisation

We have,
$\begin{array}{rcl}M& =& \chi H\\ & =& \left({\mu }_r-1\right)H\\ & =& \left(500-1\right)500\\ & =& 2.495\times {10}^5\\ & \approx & 2.5\times {10}^5\text{A/m}\end{array}$

Therefore, the magnetisation of the solenoid is $2.5\times {10}^5\text{A/m}$.