Magnetism and Matter — Questions & Answers

Sample questions from Magnetism and Matter

1. Q1. A small iron piece is strongly attracted by a magnet at room temperature. If the iron is heated to 800 °C (above its Curie point of 770 °C), the attraction:

   • A.Becomes much stronger
   • B.Becomes very weak, since iron is now only paramagnetic✓
   • C.Reverses to repulsion
   • D.Remains exactly the same
   Solution

   Above T_c the domain alignment is destroyed by thermal agitation and iron becomes paramagnetic with χ ~ 10^-3 instead of ~10^3. A paramagnet is still weakly attracted, so the pull does not vanish or reverse, but it becomes extremely small.

2. Q2. At a certain place the horizontal component of the Earth's field is 3.2 x 10^-5 T and the dip is 60 degrees. A dip needle constrained to a vertical plane containing the magnetic meridian will point along a direction whose total field is:

   • A.1.6 x 10^-5 T
   • B.6.4 x 10^-5 T✓
   • C.5.5 x 10^-5 T
   • D.3.2 x 10^-5 T
   Solution

   B = B_H/cos(dip) = 3.2x10^-5/cos60 = 6.4x10^-5 T. The vertical component is B_H tan60 = 5.5x10^-5 T, so choosing that value confuses B_V with the total field.

3. Q3. A ferromagnetic sample's hysteresis loop is measured at two different maximum applied field amplitudes: a SMALL amplitude (not reaching full saturation) and a LARGE amplitude (reaching full saturation). Compared to the small-amplitude loop, the large-amplitude (saturating) loop generally has:

   • A.A larger enclosed area (and hence more energy dissipated per cycle)✓
   • B.Exactly the same enclosed area, regardless of amplitude
   • C.A smaller enclosed area
   • D.No hysteresis loop at all, only a single straight line
   Solution

   As the maximum applied field amplitude increases (approaching and reaching saturation), the hysteresis loop generally becomes WIDER (larger area), since more domains are driven through irreversible wall-motion and reorientation processes, dissipating more energy per cycle -- a small-amplitude loop (minor loop, not reaching saturation) is correspondingly narrower with less enclosed area. A student who assumes the loop shape/area is independent of the applied amplitude picks B.

4. Q4. A short bar magnet's dipole moment can be experimentally determined using EITHER the oscillation method (measuring the period of small oscillations in a known field) OR the deflection method (measuring the deflection of a small compass needle placed near the magnet, in a known field). Using BOTH methods together (rather than just one) allows an experimenter to determine:

   • A.Both the unknown dipole moment m AND the unknown field B SEPARATELY, rather than just their product or ratio✓
   • B.Only the dipole moment, never the field, regardless of how many methods are combined
   • C.Nothing more than either method alone, since they measure the exact same quantity
   • D.The material's Curie temperature directly
   Solution

   The oscillation method's period formula effectively gives the PRODUCT mB (since T=2 pi sqrt(I/(mB)) allows solving for mB once T is measured), while the deflection method's formula effectively gives the RATIO m/B (from the tangent-law deflection formula relating the magnet's field at the compass to the ambient field B). Having BOTH the product mB and the ratio m/B from the two separate experiments allows solving simultaneously for m and B INDIVIDUALLY (m = sqrt[(mB)x(m/B)], B = sqrt[(mB)/(m/B)]), which neither method alone can provide (each alone gives only a product or a ratio, not both unknowns separately). A student who thinks the two methods are redundant (measuring the same combined quantity) picks C.

5. Q5. For the same bar magnet cut in two equal halves (as above), the new POLE STRENGTH (q_m) of each half, compared to the original pole strength, is:

   • A.Quartered
   • B.Halved
   • C.Doubled
   • D.Unchanged (the same as the original)✓
   Solution

   Pole strength q_m is essentially the magnetization times the cross-sectional area (an intensive-like property related to the material's magnetization density and geometry perpendicular to the cut), and cutting the magnet along its length (perpendicular cut, same cross-section) does not change this magnetization or cross-section, so the pole strength remains UNCHANGED for each half -- it is the dipole MOMENT (which also depends on the now-halved length) that changes, not the pole strength itself. A student who conflates pole strength with dipole moment (assuming both change the same way) picks B.

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