Flashcards · 7408 · Topic 7

Fields and their consequences flashcards

32 cards on Topic 7, subtopics 3.7.1 to 3.7.5. Pick a subtopic or study them all.

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Force field: A region in which a body experiences a non-contact force.
What produces gravitational, electric and magnetic fields?: Gravitational: mass. Electric: static charge. Magnetic: moving charge.
Gravitational vs electrostatic fields: one similarity and one difference: Similar: both obey inverse-square laws and use field lines, potential and equipotential surfaces. Different: masses always attract; charges can attract or repel.

Newton's law of gravitation and field strength in a radial field: F = Gm₁m₂/r². g = F/m; for a radial field g = GM/r², with r measured from the centre of mass.
Gravitational potential: definition, and why it is negative: The work done per unit mass in bringing a mass from infinity to that point. V = −GM/r. It is zero at infinity and negative elsewhere because the force is attractive.
Equipotential surfaces: No work is done moving along them; they are perpendicular to field lines.
Derive T² ∝ r³ for a circular orbit: GMm/r² = mv²/r. Substitute v = 2πr/T and rearrange: T² = (4π²/GM)r³. 4π²/GM is constant for one central mass.
Kinetic, potential and total energy of an orbiting satellite: Ek = GMm/2r, Ep = −GMm/r, total = −GMm/2r.
Geostationary orbit: Earth-synchronous (24 h period), in the equatorial plane, moving west to east, radius about 4.2 × 10⁷ m. Fixed dishes can point at it.
Escape velocity: v = √(2GM/R), from ½mv² = GMm/R: the kinetic energy equals the energy needed to reach infinity.
Link between g and the V–r graph: g = −ΔV/Δr: g is minus the gradient of the V–r graph. The area under a g–r graph gives the potential difference.

Coulomb's law: F = (1/4πε₀) Q₁Q₂/r², for point charges in a vacuum (air counts as a vacuum). A charged sphere acts as if its charge were at its centre.
Electric field strength: definition, radial field and uniform field: E = F/Q. Radial: E = (1/4πε₀) Q/r². Uniform (parallel plates): E = V/d.
Absolute electric potential: Work done per unit positive charge in bringing it from infinity. Positive near a positive charge, negative near a negative one. Radial: V = (1/4πε₀) Q/r.
Path of a charged particle entering a uniform electric field at right angles: A parabola: constant velocity along the plates, constant acceleration (a = QE/m) across them.
Gravitational vs electrostatic force between a proton and an electron: The gravitational force is negligible: smaller by a factor of order 10³⁹.

Capacitance, and capacitance of a parallel-plate capacitor: C = Q/V (farads). C = Aε₀εᵣ/d, where εᵣ is the relative permittivity (dielectric constant).
Dielectric action: Polar molecules rotate to line up with the field. Their own field opposes the applied field, so the pd falls for a given charge and C rises.
Energy stored by a capacitor: The area under the charge–pd graph: E = ½QV = ½CV² = ½Q²/C.
Time constant: what fraction remains after one RC on discharge, and is reached after one RC on charge?: Discharge: about 37% left. Charge: about 63% reached.
Time constant vs half-time: Time constant = RC. Half-time = 0.69RC.
Required practical 9: the graph for a capacitor discharge: Plot ln V against t. Gradient = −1/RC.
Discharge equation, and R = 10 kΩ, C = 100 μF: find RC: Q = Q₀e^(−t/RC) (V and I follow the same form). RC = 10 × 10³ × 100 × 10⁻⁶ = 1.0 s.

The tesla: 1 T gives a force of 1 N on 1 m of wire carrying 1 A perpendicular to the field (F = BIl).
Charged particle moving at right angles to a magnetic field: F = BQv, perpendicular to the velocity, so no work is done: constant speed in a circle of radius r = mv/BQ.
Why can a cyclotron use a fixed-frequency alternating pd?: The time per orbit, 2πm/BQ, does not depend on speed.
Magnetic flux and flux linkage: Φ = BA (webers). Flux linkage NΦ = BAN cos θ, where θ is the angle between the field and the normal to the coil.
Faraday's law and Lenz's law: Faraday: induced emf = rate of change of flux linkage (ε = NΔΦ/Δt). Lenz: the induced current opposes the change producing it.
Emf of a rotating coil, and when it is greatest: ε = BANω sin ωt. It is maximum when the plane of the coil is parallel to B (flux linkage zero).
Peak 325 V sinusoidal supply: find the rms voltage: V_rms = V₀/√2 = 325 ÷ 1.41 ≈ 230 V. (Sinusoidal waveforms only.)
Transformer equation and causes of energy loss: Nₛ/Nₚ = Vₛ/Vₚ. Losses: eddy currents (reduced by a laminated core), coil resistance, magnetising the core, flux leakage.
Why is electricity transmitted at high voltage?: For the same power, high voltage means low current, so the I²R loss in the cables is low.