Question

An iron rod of volume ${10}^{-3}{\text{m}}^3$ an drelative permiability $1000$ is placed as core in a solenoid with $10\text{turns/cm}$. If a current of $0.5\text{A}$ is passed through the solenoid, then the magnetic of the rod will be nearly

• A. $50\times {10}^2{\text{Am}}^2$
• B. $5\times {10}^2{\text{Am}}^2$
• C. $500\times {10}^2{\text{Am}}^2$
• D. $0.5\times {10}^2{\text{Am}}^2$

Answer 1

The correct option is B $5\times {10}^2{\text{Am}}^2$

Given,

Volume of iron, $V={10}^{-3}{\text{m}}^3$
Relative permeability, ${\mu }_r=1000$
Number of turns per unit length, $n=10$
Magnetic moment of an iron core solenoid,

$M=({\mu }_r-1)\times NiA$
$\Rightarrow M=({\mu }_r-1)\times Ni\frac{V}{l}\Rightarrow M=({\mu }_r-1)\times \frac{N}{l}iV$
$\Rightarrow M=999\times \frac{10}{{10}^{-2}}\times 0.5\times {10}^{-3}=499.5\approx 500.$