Question 4: Magnetism and Matter

Question

A solenoid has a core made of material with relative permeability 400 . The magnetic field produced in the interior of solenoid is 1.0 T . The magnetic intensity in SI units is $\alpha 	imes 10^5$. The value of $\alpha$ is $\_\_\_\_$ .
(Free space permeability $\mu_0=4 \pi 	imes 10^{-7}$ SI units.)

Accepted Answer

For a magnetic material,
$$ B=\mu H $$
where
$$ \mu=\mu_r \mu_0 $$
Given:
$$ B=1.0\ 	ext{T}, \quad \mu_r=400, \quad \mu_0=4\pi 	imes 10^{-7} $$
So,
$$ H=\frac{B}{\mu_r \mu_0} $$
Substituting the values,
$$ H=\frac{1}{400 	imes 4\pi 	imes 10^{-7}} $$
$$ H=\frac{1}{1600\pi 	imes 10^{-7}} $$
$$ H=\frac{10^7}{1600\pi} $$
$$ H=\frac{10^4}{1.6\pi} $$
$$ H=\frac{6250}{\pi} $$
Now write it in the form $\alpha 	imes 10^5$:
$$ H=\frac{6250}{\pi}=\frac{1}{16\pi}	imes 10^5 $$
Therefore,
$$ \alpha=\frac{1}{16\pi} $$
So, the correct option is:
$$ \boxed{\frac{1}{16\pi}} $$
Option B

Answer

$\frac{25}{\pi}$

Answer

$\frac{1}{16 \pi}$

Answer

$\frac{1}{\pi}$

Answer

$\frac{1}{4 \pi}$

Magnetism and Matter

A solenoid has a core made of material with relative permeability 400 . The magnetic field produced in the interior of solenoid is 1.0 T . The magnetic intensity in SI units is \alpha \times 10^5. The value of \alpha is \_\_\_\_ . (Free space permeability \mu_0=4 \pi \times 10^{-7} SI units.)

Choose the correct answer: