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Physics - Magnetic and Superconducting Materials - Important Solved Problems(Sum): Magnetic and Superconducting Materials

**SOLVED PROBLEMS**

**A paramagnetic material has a magnetic field
intensity of 10 ^{4} Am^{–1}. If the susceptibility of the
material at room temperature is 3.7 × 10^{–5}. Calculate the
magnetization and flux density in the material.**

**A
magnetic material has a magnetization of 2300 A m ^{–1} and produces a
flux density of 0.00314 Wb m^{–2}. Calculate the magnetizing force and
the relative permeability of the material.**

**Solution :**

*Given
data:*

Magnetization
M = 2300 A m^{–1}

Flux
density B = 0.00314 Web m^{–2}.

**A paramagnetic material has FCC structure with a
cubic edge of 2.5 A°. If the saturation value of magnetization is 1.8 × 10 ^{6}
A m^{–1}, Calculate the magnetization contributed per atom in Bohr
magnetrons.**

**The saturation magnetic induction of Nickel is 0.65
Wb m ^{–2}. If the density of Nickel is 8906 kg m^{–3} and its
atomic weight is 58.7, calculate the magnetic moment of the Nickel atom in Bohr
magnetron. **

**Solution:**

*Given
data:*

Saturation
magnetic induction of Nickel

**In a magnetic material the field strength is found
to be 10 ^{6} A m^{–1}. If the magnetic susceptibility of the
material is 0.5 × 10^{–5}, calculate the intensity of magnetization and
flux density in the material.**

**A superconducting tin has a critical temperature of
3.7 K at zero magnetic field and a critical field of 0.0306 Tesla at 0 K. Find
the critical field at 2 K.**

**7.** **Calculate the critical current and current
density for a wire of a lead having a diameter of 1 mm at 4.2 K. The critical
temperature for lead is 7.18 K and H = 6.5 × 10 ^{4 }A m^{–1}.**

**
****Prove
that susceptibility of superconductor is -1 and relative permeability is zero.**

**
****Find the
critical current which can pass through a long thin superconducting wire of
aluminum of diameter 2 mm, the critical magnetic field for aluminum is 7.9 × 10 ^{3}
A m^{–1}.**

**The superconducting transistion temperature of Lead
is 7.26 K. The initial field at 0 K is 64 × 10 ^{3} Amp m^{–1}.
Calculate the critical field at 5 K.**

**A magnetic field of 2000 Amp m ^{–1} is
applied to a material which has a susceptibility of 1000. Calculate the (i)
Intensity and (ii) Flux density.**

**The superconducting transition temperature of lead
of 7.26 K. The initial field at 0 K is 64 × 10 ^{3} Amp m^{–1}.
Calculate the critical field at 5 K.**

**The magnetic field strength of Silicon is 1500 Amp
m ^{–1}. If the magnetic susceptibility is (–0.3 × 10^{–5}),
calculate the magnetization and flux density in Silicon.**

**14. Calculate the critical current which can flow
through a long thin super conducting wire of diameter 1 mm. The critical
magnetic field is 7.9 × 10 ^{3} Amp m^{–1}.**

**ASSIGNMENT
PROBLEMS**

1.The
saturation value of magnetization of iron is 1.76 × 10^{6} A m^{–1}.
Iron had body centered cubic structure with an elementary edge of 2.86
Å.Calculate the average number of Bohr magnetrons contributed to the
magnetization per atom.

**(Ans: 2.2 Bohr magnetron per
atom)**

2.The
magnetic field intensity of a ferric oxide piece is 10^{6} A m^{–1}.
If the susceptibility of the material at room temperature is 10.5 × 10^{–3},
calculate the flux density and magnetization of the material.

**(Ans: B = 1.259 T and M = 1500 A
m ^{–1} )**

3. A magnetic material has a magnetization of 3000 A m^{–1}
and flux density of 0.044 Wb m^{–2}. Calculate the magnetic force and
the relative permeability of the

material. **(Ans: M = 203 and** _{r }**= 17.26)**

Calculate the magnetic filed in the lead at 5 K, if
it’s critical magnetic field at 0 K H0 = 8 × 10^{5} A m^{–1},
and transition temperature T_{C} = 7.26 K

**(Ans: 4.2 × 10 ^{5} A m^{–1})**

The critical temperature T_{C} for mercury
with isotopic mass 199.5 is 4.185 K. Calculate its critical Temperature, when
it’s isotopic masses changes to 203.4.

**(Ans: 4.139 K)**

Calculate
the critical current which can flow though a long thin superconducting wire of
aluminum of diameter 1 mm. The critical magnetic field for aluminum is 7.9 × 10^{3}
A m^{–1}.

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