7: Fields & Their Consequences Flashcards
Concept of a Force Field
Region in which a body experiences a non-contact force
Force fields arise from ____
The interaction of mass, of static charge and between moving charges
Similarities & Differences between Gravitational & Electrostatic Forces (1:4, 1:1)
- Similarities:
• Both have inverse-square laws
• Use field lines
• Use of potential concept
• Equipotential surfaces - Differences:
• Masses always attract, but charges may attract or repel
Gravity
Universal attractive force between all matter
Magnitude of Force between Two Point Masses
F = G m₁ m₂ / r² where G is the gravitational constant
g
Force per unit mass as defined by g = F / m
Magnitude of g in Radial Field
g = G M / r²
Representation of Gravitational Field by Gravitational Field Lines
https://qph.fs.quoracdn.net/main-qimg-1e788e321185dc777fa96ced46727c30
Gravitational Potential
The work that needs to be done to move a unit mass from infinity to the point
The gravitational potential at an ____ from the mass will be ____
Infinite distance, zero
Gravitational Potential Difference
The energy needed to move a unit mass between two points with different gravitational potentials
Work Done in Moving Mass m
ΔW = m ΔV
Gravitational Equipotential Surfaces
They contain all the points with the same gravitational potential
No ____ when moving along ____
Work is done, an equipotential surface
V in Radial Field
V = - GM / r
Significance of Negative Sign in Gravitational Potential
Gravitational potential is 0 at ∞ so work needs to be done against the field to reach ∞
Graphical Representation of Variation of g with r
https://www.a-levelphysicstutor.com/images/fields/g-graph01.jpg
Graphical Representation of Variation of V with r
https://www.cyberphysics.co.uk/Q&A/KS5/gravitation/q5a.png
Relation of V & g
g = - ΔV / Δr
Area Under a Graph of g against r
ΔV
Orbital period and speed related to ____
Radius of circular orbit
Derivation of T² ∝ r³ (5)
- Force between two masses: F = G m₁ m₂ / r²
- Centripetal force: F = m₂ v² / r
- m₂ v² / r = G m₁ m₂ / r²
⇒ v = √(G m₁ / r) - v = 2 π r / T (distance / time)
- 2 π r / T = √(G m₁ / r)
⇒ T² / 4 π² r² = r / G m₁
⇒ T² = (4 π² / G m₁) r³
∴ T² ∝ r³
Escape Velocity
The minimum speed an object needs to leave a gravitational field and not fall back due to gravitational attraction
Escape Velocity Formula (3)
- Kinetic energy lost = Gravitational potential energy gained
- ½ m v² = G M m / r
- v = √(2 G M / r)
Energy Considerations for an Orbiting Satellite (3)
- An orbiting satellite has kinetic and potential energy – its total energy is always constant
- In a circular orbit, orbital speed and distance above the mass are constant so kinetic and potential energy are both constant
- In an elliptical orbit, a satellite will speed up as its orbital radius decreases so kinetic energy increases as potential energy decreases
Synchronous Orbit
When an orbiting object has an orbital period equal to the rotational period of the object it is orbiting
Geostationary Orbit (4)
- Geostationary satellites are always above the same point on Earth
- Their orbit is in the plane of the equator
- Their orbital period is the same as Earth’s rotational period (synchronous orbit and same angular speed)
- Given their orbital period is 24 hours, orbital radius can be calculated as ~42 000 km
Low Orbits (3)
- Low orbiting satellites are cheaper to launch and require less powerful transmitters so they’re useful for communications
- Imaging satellites have low orbits for imaging and monitoring weather
- As the planet and the satellite rotate at different angular speeds, the satellite doesn’t stay over the same point on Earth so it can cover the whole of the surface
Force between Point Charges in a Vacuum
F = (1 / 4 π ε₀) ((Q₁ Q₂) / r²)
Permittivity of Free Space
ε₀ is the opposition offered against the formation of an electric field in a vacuum
Comparison of Magnitude of Gravitational and Electrostatic Forces between Subatomic Particles
The distance between the particles is small, but the mass of the particles is also small so gravitational forces are small whereas electrostatic forces are big
Representation of Electric Fields by Electric Field Lines (2)
Uniform field: https://th.bing.com/th/id/OIP.cgxeo3AL1zJpHRVbgAeLzQHaFj
Radial field: https://i.ytimg.com/vi/c8H1j9LWjls/maxresdefault.jpg
Electric Field Strength
Force per unit charge
E
Force per unit charge defined by E = F / Q
Magnitude of E in a Uniform Field
E = V / d
Derivation from Work Done Moving Charge between Plates (3)
- E = F / Q and E = ΔV / d
- F / Q = ΔV / d
- F d = Q ΔV
Trajectory of Moving Charged Particle Entering a Uniform Electric Field Initially at Right Angles (3)
- A charged particle feels a constant force parallel to the electric field lines
- If it is positively / negatively charged, the force is the same / opposite direction to the field lines
- This causes the particle to accelerate at right angles to its original motion so it follows a parabolic path