Magnetism

• A magnet attracts both an unmagnetized piece of iron AND the opposite pole of another magnet due to magnetic induction.
• Therefore, attraction alone cannot determine whether the test piece is a magnet or merely an unmagnetized magnetic substance.
• In contrast, repulsion occurs exclusively between two like poles of two magnets.
• Hence, repulsion is the only foolproof test to confirm that a given material is a magnetized body.

• By definition, the tangent drawn at any point on a magnetic field line represents the unique direction of the magnetic force at that location.
• If two field lines were to intersect, two different tangents could be drawn at the single point of intersection.
• This would mean that a compass needle placed at that point would have to point in two different directions simultaneously, which is physically impossible.
• Hence, magnetic field lines can never cross or intersect.

• Neutral Point: A point where the magnetic field produced by a magnet is strictly equal in magnitude and opposite in direction to the horizontal component of Earth's magnetic field ($B_{\text{magnet}} = B_H$). The net resultant magnetic field is zero ($B_{\text{net}} = 0$).
• Location for N-pole pointing North: The neutral points lie symmetrically on the Broadside-on line (Equatorial line), situated to the East and West of the magnet on its perpendicular bisector.

• (i) Dip = $0^\circ$: At the Magnetic Equator (where the total magnetic field of the Earth is completely horizontal: $B_V = 0, B_H = B$).
• (ii) Dip = $90^\circ$: At the Magnetic Poles (where the magnetic field lines plunge vertically into or out of the Earth: $B_H = 0, B_V = B$).

• Soft Iron: Easily magnetized and easily demagnetized (high susceptibility, low retentivity). Used as cores in electromagnets, electric bells, telephone earpieces, and transformers.
• Steel: Difficult to magnetize, but once magnetized, retains its magnetism permanently (high retentivity and high coercivity). Used for manufacturing permanent bar magnets, compass needles, and audio loudspeakers.

• When an unmagnetized iron nail is brought near the North pole of a bar magnet, the magnet first induces an opposite South pole on the near end of the nail and a similar North pole on the far end via magnetic induction.
• Because the unlike induced South pole is closer to the magnet's North pole than the like North pole, the force of attraction exceeds the force of repulsion.
• Thus, magnetic induction occurs first, and attraction occurs as a consequence.

• (i) Cut Transversely: Two smaller bar magnets are formed, each having its own North and South pole. The pole strength remains unchanged, but the magnetic length is halved, so the magnetic dipole moment is halved ($M' = \frac{M}{2}$).
• (ii) Cut Longitudinally: Two thinner bar magnets are formed. The magnetic length remains the same, but the pole strength is halved, so the magnetic dipole moment is also halved ($M' = \frac{M}{2}$). In both cases, isolated magnetic monopoles are never produced.

• Magnetic Declination: The acute angle between the true Geographic Meridian (true North-South plane) and the Magnetic Meridian (plane of Earth's magnetic axis) at a given place on Earth.
• Why compass does not point to true North: Earth's magnetic dipole axis is tilted at an angle of approximately $11.3^\circ$ relative to its geographic rotational axis. Therefore, a magnetic compass aligns along the magnetic meridian, pointing slightly East or West of true Geographic North by the angle of declination.