Question 7: Magnetism and Matter

Question

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility $\chi_{\mathrm{Mg}}=1.2 	imes 10^{-5}$ ) is :

Accepted Answer

The percentage change in the magnetic field (B) when the space within a current-carrying solenoid is filled with magnesium is calculated as follows:
We start by using the formula for percentage change in the magnetic field:
$ \% 	ext{ change in } B = \frac{B_{	ext{new}} - B_{	ext{old}}}{B_{	ext{old}}} 	imes 100\% $
Substituting the expressions for the magnetic field, we have:
$ = \frac{\mu n i - \mu_0 n i}{\mu_0 n i} 	imes 100\% = \frac{\mu - \mu_0}{\mu_0} 	imes 100\% $
Where:
$\mu$ is the permeability of the material inserted (here, magnesium).
$\mu_0$ is the permeability of free space.
$n$ is the number of turns per unit length of the solenoid.
$i$ is the current through the solenoid.
Given that the relationship between the permeability of the medium ($\mu$) and relative permeability ($\mu_r$) is:
$ \mu = \mu_0 \mu_r $
We can simplify this to:
$ = \frac{\mu_0 \mu_r - \mu_0}{\mu_0} 	imes 100\% $
Which reduces to:
$ = (\mu_r - 1) 	imes 100\% $
The relative permeability $\mu_r$ is equal to $1 + \chi$, where $\chi$ is the magnetic susceptibility. Thus, we have:
$ = \chi 	imes 100\% $
When magnesium is used, with a magnetic susceptibility $\chi_{	ext{Mg}} = 1.2 	imes 10^{-5}$, the calculation becomes:
$ = 1.2 	imes 10^{-5} 	imes 100\% = 1.2 	imes 10^{-3}\% $
Therefore, the percentage increase in the magnetic field when the solenoid is filled with magnesium is $1.2 	imes 10^{-3}\%$.

Answer

$\frac{5}{3} 	imes 10^{-5} \%$

Answer

$\frac{5}{6} 	imes 10^{-4} \%$

Answer

$\frac{5}{6} 	imes 10^{-5} \%$

Answer

$\frac{6}{5} 	imes 10^{-3} \%$

Magnetism and Matter

The percentage increase in magnetic field (B) when space within a current carrying solenoid is filled with magnesium (magnetic susceptibility \chi_{\mathrm{Mg}}=1.2 \times 10^{-5} ) is :

Choose the correct answer: