Question

A solenoid has a core of a material with relative permeability of $500$. The windings of the solenoid are insulated from the core and carry a current of $2$A. If the number of turns is $1000$ per meter, then magnetisation is?

• A. $7.78\times {10}^5$A $m^{-1}$
• B. $8.88\times {10}^5$A $m^{-1}$
• C. $9.98\times {10}^5$A $m^{-1}$
• D. $10.2\times {10}^5$A $m^{-1}$

Answer 1

The correct option is C $9.98\times {10}^5$A $m^{-1}$

As $B={\mu }_o(M+H)$
magnetisation, $M=\frac{(B-{\mu }_{o}H)}{{\mu }_o}$
then $M=\frac{{\mu }_o{\mu }_{r}H-{\mu }_{o}H}{{\mu }_o}=({\mu }_r-1)H$ $(\because B={\mu }_o{\mu }_{r}H)$
Here, ${\mu }_r=500$ and $H=nI=1000\times 2=2000A{m}^{-1}$
$\therefore M=(500-1)H=499\times 2000$
or $M=9.98\times {10}^{5}A{m}^{-1}$.