Magnetism — Set 4

Correct Answer: B. Magnetic poles usually occur in pairs

• **Magnetic poles usually occur in pairs** = Every magnet has both N and S poles; cutting a magnet creates two smaller magnets each with both poles — magnetic monopoles have not been observed. • **∇·B = 0 (no magnetic monopoles in Maxwell's equations)** — Magnetic field lines form closed loops; an isolated pole would violate this law. • 💡 Wrong-option analysis: Magnetic poles instantly turn into electric charges: poles do not transform into charges; Poles exist only at absolute zero: poles exist at all temperatures; Magnets always lose magnetism in air: magnetism is unaffected by air at normal conditions.

Correct Answer: D. A smaller magnet with both poles

• **A smaller magnet with both poles** = Breaking a magnet creates two smaller magnets; the domain structure re-forms poles at the new ends. • **Each fragment: N + S pole; this repeats at any scale** — Demonstrates that magnetic monopoles do not exist in matter. • 💡 Wrong-option analysis: Only a north pole: each piece always has both poles; Only a south pole: same reason; Non-magnetic iron: the pieces retain domain alignment and remain magnets.

Correct Answer: C. Magnetic field lines never intersect.

• **Magnetic field lines never intersect.** = Field lines cannot cross because that would imply two different field directions at one point, which is physically impossible. • **Unique field direction at every point → lines never cross** — This is true for any vector field including electric fields. • 💡 Wrong-option analysis: Magnetic field lines always start at the center only: field lines form closed loops around magnets; Magnetic field lines are always straight: they curve and form loops; Magnetic field lines exist only inside magnets: field lines exist outside magnets too — that is how a compass works.

Correct Answer: D. Strength of the magnetic field

• **Strength of the magnetic field** = The density (closeness) of field lines represents field magnitude; lines are densest near the poles where B is strongest. • **High line density ↔ strong B; low density ↔ weak B** — Near poles of bar magnet: dense lines; far away: sparse lines. • 💡 Wrong-option analysis: Mass of the magnet: mass affects strength but the diagram convention is about line density; Color of the material: color is not represented by field line density; Temperature of the magnet: temperature affects magnetization but is not shown by line density.

Correct Answer: B. South to north

• **South to north** = Inside the magnet, field lines run from S to N, forming closed loops with the external path N to S. • **Internal: S → N; external: N → S (closed loops)** — Continuity of field lines reflects that ∇·B = 0. • 💡 Wrong-option analysis: Upward only: direction depends on magnet orientation; North to south: that is the direction outside the magnet; East to west only: no fixed cardinal direction for field lines.

Correct Answer: B. South pole

• **South pole** = The north-seeking end of a compass (its N pole) is attracted to a magnetic south pole; Earth's geographic north region behaves like a magnetic south pole. • **Earth's magnetic S pole is near geographic N** — Earth's magnetic north pole (which attracts S ends of compass) is near geographic south. • 💡 Wrong-option analysis: North pole: like poles repel; if geographic north were magnetic N, compass N would be repelled; Neutral point: a neutral point has zero field, a compass would not orient; No pole at all: Earth definitely has magnetic poles.

Correct Answer: C. Magnetic equator

• **Magnetic equator** = At the magnetic equator, Earth's field is horizontal (no vertical component), so the dip angle is zero. • **Dip = 0° at magnetic equator; 90° at magnetic poles** — Dip needle lies horizontal only at the magnetic equator. • 💡 Wrong-option analysis: Geographic poles: geographic poles have large dip but not necessarily zero; Magnetic poles: dip = 90° at magnetic poles, not zero; Any place on Earth: dip varies from 0° to 90°, not zero everywhere.

Correct Answer: D. Magnetic poles

• **Magnetic poles** = At the magnetic poles, Earth's field is vertical (no horizontal component), so the dip angle is 90°. • **Dip = 90° at magnetic poles; B is purely vertical** — A dip needle stands vertical at magnetic poles. • 💡 Wrong-option analysis: Magnetic equator: dip = 0° there, not 90°; Tropic of Cancer: dip is large but not exactly 90°; International Date Line: a geographic line with no special magnetic significance.

Correct Answer: B. Ampere-meter squared

• **Ampere-meter squared** = Magnetic dipole moment m = NIA (for a current loop); units = A·m². • **m = NIA in A·m²** — For a bar magnet, m = pole strength × length; stronger m means stronger magnet. • 💡 Wrong-option analysis: Weber: unit of magnetic flux (Φ); Tesla: unit of magnetic flux density (B); Newton per coulomb: that equals volt per meter (V/m), the unit of electric field.

Correct Answer: C. Φ = BA cosθ

• **Φ = BA cosθ** = Flux Φ = B · A = BA cosθ, where θ is the angle between B and the area normal (area vector). • **Φ_max = BA when θ = 0 (B ⊥ surface plane)** — Faraday's law: induced EMF = −dΦ/dt. • 💡 Wrong-option analysis: Φ = B + A: adding quantities with different units is meaningless; Φ = B/A: division gives flux density, not flux; Φ = BA sinθ: sin applies when angle is from the surface itself (not the normal), but standard form uses cosθ from the normal.