Solveeit Logo
Login

Question

Question: The magnetic susceptibility of uranium is \(40 \times {10^{ - 6}}\).It’s permeability is ___________...

The magnetic susceptibility of uranium is 40×10−640 \times {10^{ - 6}}.It’s permeability is ______________ ?
a) 1.0004 μ0a){\text{ 1}}{\text{.0004 }}{\mu _0}
b) 0.9996 μ0b){\text{ 0}}{\text{.9996 }}{\mu _0}
c) 41×10−5c){\text{ 41}} \times {\text{1}}{{\text{0}}^{ - 5}}
d) 39×10−5d){\text{ 39}} \times {\text{1}}{{\text{0}}^{ - 5}}

Explanation

Solution

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:
μr=1+XM{\mu _r} = 1 + {X_M}
XM{X_M} refers to magnetic susceptibility
μr{\mu _r}refers to relative permeability
μr=μμ0{\mu _r} = \dfrac{\mu }{{{\mu _0}}}
μr{\mu _r}refers to relative permeability
μ\mu refers to permeability
μ0{\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
XM=40×10−6{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
μr=1+XM{\mu _r} = 1 + {X_M}
Now substituting the value of XM{X_M} in the above question we will get
μr=1+40×10−6{\mu _r} = 1 + 40 \times {10^{ - 6}}
40×10−640 \times {10^{ - 6}} converting into points we will get
40×10−6=0.0004040 \times {10^{ - 6}} = 0.00040
Now using this in the prime equation we gets
μr=1+0.0004{\mu _r} = 1 + 0.0004
μr=1.0004{\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 μr=1.0004{\mu _r} = 1.0004

Now by substituting μ0{\mu _0} and μr{\mu _r} we will get
μr=μμ0{\mu _r} = \dfrac{\mu }{{{\mu _0}}}
μ=μrμ0\mu = {\mu _r}{\mu _0}
After taking μ\mu on other side we only have to insert values
μ=1.0004μ0\mu = 1.0004{\mu _0}
Hence, the correct option is a) 1.0004 μ0a){\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.