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D. Fields

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  1. D.1 Gravitational fields

    1. • Kepler’s three laws of orbital motion.

    2. • Universal gravitation: F=Gm1m2/r^2 for point masses.

    3. • Extended bodies can be treated as point masses only under suitable conditions.

    4. • Gravitational field strength: g=F/m=GM/r^2.

    5. • Gravitational field lines.

    6. • Gravitational potential energy is work to assemble masses from infinite separation.

    7. • Two-body gravitational potential energy: Ep=-Gm1m2/r.

    8. • Gravitational potential: Vg=-GM/r, zero at infinity.

    9. • Field strength is potential gradient: g=-ΔVg/Δr.

    10. • Work in gravitational field: W=mΔVg.

    11. • Equipotential surfaces for gravitational fields.

    12. • Relationship between equipotential surfaces and gravitational field lines. • Equipotential surfaces are perpendicular to field lines.

    13. • Escape speed: vesc=sqrt(2GM/r).

    14. • Circular orbital speed: vorbital=sqrt(GM/r).

    15. • Small atmospheric drag changes both height and speed of an orbiting body.

  2. D.2 Electric and magnetic fields

    1. D.2.1—Electric charge forces

      • Direction of forces between the two types of electric charge.

    2. D.2.2—Coulomb’s law

      • Coulomb’s law: F=kq1q2/r^2 for point charges; k=1/(4πε0).

    3. D.2.3—Charge conservation

      • Conservation of electric charge.

    4. D.2.4—Millikan experiment

      • Millikan’s experiment as evidence for quantization of electric charge.

    5. D.2.5—Charge transfer

      • Charge transfers by friction, electrostatic induction or contact. • Grounding can remove or add charge.

    6. D.2.6—Electric field strength

      • Electric field strength: E=F/q.

    7. D.2.7—Electric field lines

      • Electric field lines.

    8. D.2.8—Field-line density

      • Relationship between field line density and field strength. • Greater field-line density indicates stronger field.

    9. D.2.9—Parallel-plate field

      • Uniform field between plates: E=V/d.

    10. D.2.10—Magnetic field lines

      • Magnetic field lines.

    11. D.2.11 (HL)—Electric potential energy

      • Electric potential energy is work to assemble charges from infinite separation.

    12. D.2.12 (HL)—Two-charge potential energy

      • Two-charge electric potential energy: Ep=kq1q2/r.

    13. D.2.13 (HL)—Electric potential as scalar

      • The electric potential is a scalar quantity with zero defined at infinity.

    14. D.2.14 (HL)—Electric potential

      • Electric potential: Ve=kQ/r, zero at infinity.

    15. D.2.15 (HL)—Electric potential gradient

      • Electric field strength is potential gradient: E=-ΔVe/Δr.

    16. D.2.16 (HL)—Work in electric fields

      • Work moving charge in electric field: W=qΔVe.

    17. D.2.17 (HL)—Electric equipotentials

      • Equipotential surfaces for electric fields. • No work is done moving along an equipotential surface.

    18. D.2.18 (HL)—Equipotentials and electric fields

      • Relationship between equipotential surfaces and electric field lines. • Equipotential surfaces are perpendicular to electric field lines.

  3. D.3 Motion in electromagnetic fields

    1. • Motion of a charged particle in a uniform electric field.

    2. • Motion of a charged particle in a uniform magnetic field.

    3. • Charged particles can move in perpendicular uniform electric and magnetic fields.

    4. • Magnetic force on moving charge: F=qvB sinθ.

    5. • Force on current-carrying conductor: F=BIL sinθ.

    6. • Force per unit length between parallel wires: F/L=μ0I1I2/(2πr). • Parallel currents attract when currents flow in the same direction.

  4. D.4 Induction

    1. • Magnetic flux: Φ=BA cosθ.

    2. • Faraday’s law: changing magnetic flux induces emf ε=-NΔΦ/Δt.

    3. • Motional emf in a straight conductor: ε=BvL.

    4. • Lenz’s law gives induced emf direction and reflects energy conservation. • Direction of induced emf opposes the change that produces it.

    5. • Rotating coil in uniform magnetic field produces sinusoidal emf.

    6. • Increasing rotation frequency increases induced emf characteristics.