Physics · Textbook solutions

Magnetic Materials

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 25 questions

11. Magnetic Materials — worked examples

4 q

Solved Examples

Worked · 4
  1. Solved Ex.11.1
    A bar magnet of moment of inertia of 500 g cm2^2 makes 10 oscillations per minute in a horizontal plane. What is its magnetic moment, if the horizontal component of earth's magnetic field is 0.36 gauss?
  2. Solved Ex.11.2
    Calculate the gyromagnetic ratio of electron (given e=1.6×10−19e = 1.6 \times 10^{-19} C, me=9.1×10−31m_{e} = 9.1 \times 10^{-31} kg).
  3. Solved Ex.11.2b
    The region inside a current carrying toroid winding is filled with Aluminium having susceptibility χ=2.3×10−5\chi = 2.3 \times 10^{-5}. What is the percentage increase in the magnetic field in the presence of Aluminium over that without it?
  4. Solved Ex.11.3
    A domain in ferromagnetic iron is in the form of cube of side 1 μ\mum. Estimate the number of iron atoms in the domain, maximum possible dipole moment and magnetisation of the domain. The molecular mass of iron is 55 g/mole and density is 7.9 g/cm3^3. Assume that each iron atom has a dipole moment of 9.27×10−249.27 \times 10^{-24} Am2^2.

Exercises

21 q

Choose the correct option

Practice · 5
  1. Choose the correct option.
    Ex Q.1 (i)
    Intensity of magnetic field of the earth at the point inside a hollow iron box is
    1. A.
      less than that outside
    2. B.
      more than that outside
    3. C.
      same as that outside
    4. D.
      zero
  2. Ex Q.1 (ii)
    Soft iron is used to make the core of transformer because of its
    1. A.
      low coercivity and low retentivity
    2. B.
      low coercivity and high retentivity
    3. C.
      high coercivity and high retentivity
    4. D.
      high coercivity and low retentivity
  3. Ex Q.1 (iii)
    Which of the following statements is correct for diamagnetic materials?
    1. A.
      μr<1\mu_{r} < 1
    2. B.
      χ\chi is negative and low
    3. C.
      χ\chi does not depend on temperature
    4. D.
      All of above
  4. Ex Q.1 (iv)
    A rectangular magnet suspended freely has a period of oscillation equal to TT. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely. Its period of oscillation is T′T', the ratio of T′/TT'/T is
    1. A.
      122\dfrac{1}{2\sqrt{2}}
    2. B.
      1/21/2
    3. C.
      22
    4. D.
      1/41/4
  5. Ex Q.1 (v)
    A magnetising field of 360 Am−1^{-1} produces a magnetic flux density (B)=0.6(B) = 0.6 T in a ferromagnetic material. What is its permeability in Tm A−1^{-1}?
    1. A.
      1/3001/300
    2. B.
      300300
    3. C.
      1/6001/600
    4. D.
      600600

Answer in brief

Practice · 7
  1. Answer in brief.
    Ex Q.2 (i)
    Which property of soft iron makes it useful for preparing electromagnet?
  2. Ex Q.2 (ii)
    What happens to a ferromagnetic material when its temperature increases above curie temperature?
  3. Ex Q.2 (iii)
    What should be retentivity and coercivity of permanent magnet?
  4. Ex Q.2 (iv)
    Discuss the Curie law for paramagnetic material.
  5. Ex Q.2 (v)
    Obtain and expression for orbital magnetic moment of an electron rotating about the nucleus in an atom.
  6. Ex Q.2 (vi)
    What does the hysteresis loop represents?
  7. Ex Q.2 (vii)
    Explain one application of electromagnet.

Solve the following

Practice · 9
  1. Ex Q.3
    When a plate of magnetic material of size 10 cm ×\times 0.5 cm ×\times 0.2 cm (length, breadth and thickness respectively) is located in magnetising field of 0.5×1040.5 \times 10^{4} Am−1^{-1} then a magnetic moment of 0.5 Am2^2 is induced in it. Find out magnetic induction in plate.
  2. Ex Q.4
    A rod of magnetic material of cross section 0.25 cm2^2 is located in 4000 Am−1^{-1} magnetising field. Magnetic flux passing through the rod is 25×10−625 \times 10^{-6} Wb. Find out (a) relative permeability (b) magnetic susceptibility and (c) magnetisation of the rod.
  3. Ex Q.5
    The work done for rotating a magnet with magnetic dipole moment mm, through 90∘90^\circ from its magnetic meridian is nn times the work done to rotate it through 60∘60^\circ. Find the value of nn.
  4. Ex Q.6
    An electron in an atom is revolving round the nucleus in a circular orbit of radius 5.3×10−115.3 \times 10^{-11} m, with a speed of 2×1062 \times 10^{6} ms−1^{-1}. Find the resultant orbital magnetic moment and angular momentum of electron. (charge on electron e=1.6×10−19e = 1.6 \times 10^{-19} C, mass of electron m=9.1×10−31m = 9.1 \times 10^{-31} kg.)
  5. Ex Q.7
    A paramagnetic gas has 2.0×10262.0 \times 10^{26} atoms/m with atomic magnetic dipole moment of 1.5×10−231.5 \times 10^{-23} A m2^2 each. The gas is at 27∘27^\circ C. (a) Find the maximum magnetization intensity of this sample. (b) If the gas in this problem is kept in a uniform magnetic field of 3 T, is it possible to achieve saturation magnetization? Why? (kB=1.38×10−23(k_{B} = 1.38 \times 10^{-23} JK−1)^{-1}) (Hint: Find the ratio of Thermal energy of atom of a gas (3/2 kBT)(3/2\, k_{B}T) and maximum potential energy of the atom (mB)(mB) and draw your conclusion)
  6. Ex Q.8
    A magnetic needle placed in uniform magnetic field has magnetic moment of 2×10−22 \times 10^{-2} A m2^2, and moment of inertia of 7.2×10−77.2 \times 10^{-7} kg m2^2. It performs 10 complete oscillations in 6 s. What is the magnitude of the magnetic field?
  7. Ex Q.9
    A short bar magnet is placed in an external magnetic field of 700 gauss. When its axis makes an angle of 30∘30^\circ with the external magnetic field, it experiences a torque of 0.014 Nm. Find the magnetic moment of the magnet, and the work done in moving it from its most stable to most unstable position.
  8. Ex Q.10
    A magnetic needle is suspended freely so that it can rotate freely in the magnetic meridian. In order to keep it in the horizontal position, a weight of 0.1 g is kept on one end of the needle. If the pole strength of this needle is 20 Am, find the value of the vertical component of the earth's magnetic field. (g=9.8(g = 9.8 m s−2)^{-2})
  9. Ex Q.11
    The susceptibility of a paramagnetic material is χ\chi at 27∘27^\circ C. At what temperature its susceptibility be χ/3\chi/3?