Question

The magnetic susceptibility of uranium is $40 \times {10^{ - 6}}$.It’s permeability is ______________ ?
$a){\text{ 1}}{\text{.0004 }}{\mu _0}$
$b){\text{ 0}}{\text{.9996 }}{\mu _0}$
$c){\text{ 41}} \times {\text{1}}{{\text{0}}^{ - 5}}$
$d){\text{ 39}} \times {\text{1}}{{\text{0}}^{ - 5}}$

Answer 1

Hint: In order to solve the question, we will first use the relation between magnetic susceptibility and relative permeability by using that we will find the relative permeability and then we will use the relation between the relative permeability, permeability and permeability of vacuum to find the permeability of uranium


Formula Used:
${\mu _r} = 1 + {X_M}$
${X_M}$ refers to magnetic susceptibility
\[{\mu _r}\]refers to relative permeability
\[{\mu _r} = \dfrac{\mu }{{{\mu _0}}}\]
\[{\mu _r}\]refers to relative permeability
\[\mu \]refers to permeability
\[{\mu _0}\] refers to permeability of vacuum and it is constant

Complete step-by-step solution:
Magnetic susceptibility of uranium is given in question that is
${X_M} = 40 \times {10^{ - 6}}$
By using the relation between magnetic susceptibility and relative permeability by using that we will find the relative permeability
${\mu _r} = 1 + {X_M}$
Now substituting the value of ${X_M}$ in the above question we will get
${\mu _r} = 1 + 40 \times {10^{ - 6}}$
$40 \times {10^{ - 6}}$ converting into points we will get
$40 \times {10^{ - 6}} = 0.00040$
Now using this in the prime equation we gets
${\mu _r} = 1 + 0.0004$
${\mu _r} = 1.0004$
Now using the relation between the relative permeability, permeability and permeability of vacuum to find the permeability of uranium
Now we have value of ${\mu _r} = 1.0004$

Now by substituting \[{\mu _0}\] and \[{\mu _r}\] we will get
\[{\mu _r} = \dfrac{\mu }{{{\mu _0}}}\]
\[\mu = {\mu _r}{\mu _0}\]
After taking \[\mu \]on other side we only have to insert values
\[\mu = 1.0004{\mu _0}\]
Hence, the correct option is $a){\text{ 1}}{\text{.0004 }}{\mu _0}$.

Note:Many of the people will make the mistake by not converting the magnetic susceptibility into points as we have done in between the question if we do not do that we cannot reach to answer and it will only lead us to difficult calculation part along with many people will write the constant value of permeability of vacuum which is not required as in question we can see that some answer consist that so we have to use it as variable.