Model Problems in Magnetic Properties of Materials

COI -1:

.

1. A coil of wire length (L) 0.45 m long and having number of turns (N) 600 carries a current (i) of 10 A. Find magnitude of magnetic field strength (H). Compute the flux density, B, if the coil is in vacuum.

Ans: Magnetic field strength, H = {Ni} / L = {600 X 10} / 0.45 = 13333.33 amp-turns/meter.Magnetic flux, B = μ0 H = 1.257 X 10 -6 X 13333.33 = 16759 X 10 -6 wb/m2.

2. Compute the flux density (B) inside a bar of chromium that is positioned within a coil of wire length (L) 0.25 m and having number of turns (N) 400 turns, carrying a current of 15 A. Magnetic permeability (μ) of chromium is 12.51X 10 -7 Henry/m.

Ans: Magnetic field strength, H = {Ni} / L = {400 X 15} / 0.25 = 24000 amp-turns/meter. Magnetic flux, B = μ0 H =12.51 X 10 -7 X 1.257 X 10 -6 X 24000 = 377401 X 10 -13 wb/m2.

3. Explain whether or not all electrons have net magnetic moment, with valid reasons.Ans: All electrons have magnetic moment due to their spin motion. (Refer text book for further explanation on spin magnetic moment of electrons).

4. Explain whether or not all atoms have net magnetic moment, with valid reasons.

5. Explain how a material exhibits magnetic moment.Ans: Every material is made of atoms. Atoms show magnetic moment due to orbital and spin motion of electrons, and spin of nucleus. Materials with atoms having unpaired electrons, aligned atomic magnetic moments show para or ferro magnetic behaviour. Materials with atoms having paried electrons show dia magnetic behaviour in the presence of external magnetic field.

6. Explain reasons why He, Ne, and Ar do not show permanent magnetism. 7. Magnetic permeability of Cobalt-Iron alloy and permalloy are 2.3 X 10 -2 H/m and

1.0 X 10 -2 H/m at room temperature. Identify the material that can easily be magnetized and provide valid reasons.

8. Following are combinations of B (Tesla) – H (A/m) values of plain carbon steel alloy: (i) 15 – 0.007, (ii) 30 – 0.033 , (iii) 50 – 0.10, (iv) 60 – 0.30. Find permeability for each combination.

9. Identify the factors that influence magnetic field strength (H) of a current (i) carrying circular coil having N number of turns. Using these factors find the ways to double the magnetic field strength associated with the coil.

10. The magnetic field strength (H) in Silicon is 1000 A/m. If the magnetic susceptibility (χ) is - 0.3 X 10-5, calculate the magnetization (M) and flux density (B) of Silicon.

COI -2:

1. The magnetic flux density (B) within a bar of some material is 0.63 Tesla at an H field of 5 X 10 5 A/m. Compute the following for this material: (a) Magnetic permeability (μ) (b) Magnetic susceptibility (χ).

2. The magnetization (M) within a bar of some metal alloy is 1.2 X 10 6 A/m at an H field of 200 A/m. Compute the following: (a) the magnetic susceptibility (χ) (b) the permeability (μ) (c) the magnetic flux density (B) within the material.

3. Compute the saturation magnetization (Ms) and saturation flux density (Bs) for iron (atomic weight: 55.8) which has a net magnetic moment per atom of 2.2 Bohr magnetons and a density of 7.87 g/cm3

4. A magnetic material has a magnetization (M) of 3300 A/m and flux density (B) of 0.0044 Wb/m2. Calculate magnetic field strength (H)and relative permeability (μr) .

5. The magnetic field intensity (H) in a piece of a magnetic material is 10 6 A/m. If the susceptibility (χ) of the material at room temperature is 1.5 X 10 -3, compute flux density (B) and magnetization (M) of material.

6. Magnetic susceptibility (χ) of a material is – 0.5 X 10 -5. If the material is subjected to magnetic field of intensity (H), 10 4 A/m, find magnetization (M) and magnetic flux density (B) of the material.

7. An iron bar magnet having coercivity of 7000 A/m is to be demagnetized. If the bar is inserted within a cyllindrical wire coil 0.25 m long and having 150 turns , find electric current required to generate necessary magnetic field.

COI -3

1. A coil of wire length (l) 0.5 m, having number of turns (N) 20, carries a current (i) of 1.0 A. (a) Compute flux density (B) if the coil is within the vacuum. (b) If a bar of iron-silicon alloy that shows B-H relation as shown in above figure, is positioned in the coil, Find flux density (B) within the coil.

2. Compare B-H curve of ferro and ferrimagnetic materials and explain properties of both the mateirals.

3. The above data are for plain carbon steel alloy. Using this data, find the values of permeability, relative permeability and susceptibility for each combination of B and H.

4. Describe coercive field strength (Hc) and remanent magnetization (Mr) and write a short note

on energy product, (BH)max, of ferromagentic material.

5. A bar of an iron-silicon alloy having the B-H behaviour shown in Figure, is inserted within a coil of wire 0.4 m long and having 50 turns, through which passes a current of 0.1 A. (a) Find

magnetic flux density, B, within the bar. (b) At this field, find permeability, relative permeability, Susceptibility and magnetization.

6. The Figure shows B-H curve of Ni-Fe alloy. Find saturation flux density, remanence and coercivity.

Also give definitions of remanence, coercivity and saturation flux density. 7. Write a short note on Anisotropic energy, Bloch wall energy, Exchange and Magnetostriction

energy of a ferromanetic material.

8. Explain easy and hard directions of magnetization of ferromagnetic material. In the plot shown above identify easy, moderate and hard directions of magnetization of BCC Iron and FCC Nickel crystals.

9. Write the ways to demagnetize magnetic materials. The Br values of Carbon steel and Tungsten steel are 0.95 and 1.05 Wb/m2 respectively. The Hc values of Carbon steel and Tungsten steel are 4000 and 5200 A/m respectively. Identify the magnetic material difficult to demagnetize.

10. Identify the materials that exhibit Hysteresis effect and explain reasons why only those materials show the Hysteresis effect. Write applications of materials that show Hysteresis effect.