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Physics > Y2: Gravitational and Electric fields > Flashcards

Y2: Gravitational and Electric fields Flashcards

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1
Q

What is a force field

A

A region in which an object experiences a non-contact force

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2
Q

What is a radial field

A

A field surrounding a central point in which the force decreases as the distance increases (Field lies move further apart).

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3
Q

What is a uniform field

A

A field in which all filed lines are parallel, and equally spaced, so the force is constant at all points within the field

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4
Q

When can gravity be considered as a uniform field

A

Close to the surface, as the field lines are (almost) parallel

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5
Q

What is Newton’s Law of gravitation

A

F = -GMm/(r^2)
(Negative as always acts towards the centre of the larger mass)

F: Magnitude of the force
G: Gravitational constant (6.67x10^-11)
M & m: Masses of the 2 objects
r: Distance between the centre of the two masses

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6
Q

What is the gravitational constant (G)

A

6.67x10^-11 (Nm^2kg^-2)

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7
Q

Why can Newton’s Law of gravitation be described as an inverse square Law

A

F ∝ 1/(r^2)
∴ The force becomes weaker at a greater distance

This is because Gravitational fields are radial:
- If a sphere is drawn around the centre of mass, radius r, all points on the sphere will experience the same force
- SA = 4π(r^2)
- ∴ x2 Radius, SA = 4π((2r)^2) = 4(4π(r^2))
- This means the surface area of the sphere increases by the square of the scale of the increase in r (SA ∝ r^2)
- The force ∝ 1/SA (field lines spread out)
- ∴F ∝ 1/(r^2)

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8
Q

What is Gravitational field strength (g)

A

The force per unit of mass of an object in a gravitational field

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9
Q

What is the equation for gravitational field strength in a uniform field

A

g = F/m
(Constant in uniform fields)

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10
Q

What is the equation for gravitational field strength in a radial field

A

g = GM/(r^2) = -ΔV/Δr
∴ Depends on the distance from the object

(Derived by dividing the force from Newton’s Law of gravitation by m)

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11
Q

What is the value for the gravitation field strength of earth (at the surface)

A

9.81 (Nkg^-1)

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12
Q

What is shown by the area under a graph of gravitational field strength against radius

A

Gravitational potential

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13
Q

What happens when gravitational fields are combined

A

Gravitational fields are vector fields, so gravitational field strengths can be added to calculate the combined effect on an object within multiple fields

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14
Q

What is gravitational potential (V)

A

The energy required to move a unit mass from infinity, to a point within the field.
(Jkg^-1)
(GPE of a unit mass)

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15
Q

Why is gravitational potential negative

A

Gravitational potential at infinity = 0
∴ Objects closer to the mass have negative potential, as work needs to be done against the field to lift them back to infinity

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16
Q

What is the equation for gravitational potential (in a radial field)

A

V = -GM/r

Energy to move the unit mass is equal to the work done
Work done = Force x distance
F = g = -GM/(r^2)
(m = 1, for unit mass)
d = r
∴ gr = (-GM/(r^2))r
∴ W = -GM/r
∴ V = -GM/r

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17
Q

What is shown by the gradient of a graph of Gravitational potential against radius

A

Gradient = -g
(-ΔV/Δr = g)

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18
Q

What is gravitational potential difference

A

The energy needed to move a unit mass between two points at different distances r from M, in a gravitational field.
(Work done per unit mass)

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19
Q

What is the equation for the gravitational potential difference (in a radial field)

A

ΔV = -GM/Δr = ΔV2-ΔV1

Potential difference = initial potential - final potential
∴ ΔV = ΔV2-ΔV1
∴ ΔV = -GM/Δr

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20
Q

What is the difference between ‘the change in gravitational potential’, and the ‘gravitational potential difference’

A
  • Change in gravitational potential =
    The difference in gravitational potential between two points in a gravitational field, where gravitational potential is 0 at infinity
  • Gravitational potential difference =
    The energy required to move a unit mass between two points in a gravitational field

Both are represented as ΔV, and are pretty much the same thing, but are defined slightly differently

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21
Q

What is the equation for work done in a gravitational field

A

ΔW = mΔV
(change in GPE)

Work done = Force x distance
F = -GMm/(r^2)
d = Δr
∴ Fd = (-GMm/(r^2))r
∴ ΔW = -GMm/r
ΔV = -GM/Δr
∴ ΔW = mΔV

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22
Q

What is gravitational potential energy

A

The energy required to move a mass m from infinity, to a point within the field. (Gravitational potential of mass m)

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23
Q

What is the equation for the gravitational potential energy in a radial field

A

Ep = -GMm/r

Work done = mΔV
Energy required is equal to the work done
∴ Ep = mΔV
ΔV = -GM/Δr
∴ Ep = -GMm/r

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24
Q

What is the equation for Gravitational potential energy in a uniform field (g is constant)

A

Ep = mgh
(Positive, as the earth’s surface is taken to be 0 close to the surface)

This is derived from the equation for Ep in a radial fields, using h (Δr) instead of r
m = m
g = GM/(r^2)
h = (Δ)r
∴ mgh = m(GM/(r^2))r
∴ GMm/r ⇒ mgh

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25
Q

What are equipotentials

A

Lines (2D) or surfaces (3D) that join together all the points within a field that have the same gravitational potential
- Are perpendicular to field lines
- Objects traveling along equipotentials have the same V
(Ep = 0)

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26
Q

What are satellites

A

Any smaller mass that orbits a larger mass, due to the gravitational ‘pull’ of the larger mass
(Gravitational force acts as centripetal force)

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27
Q

What is the equation for the orbital speed of a satellite

A

v = √(GM/r)

Centripetal force of orbit is caused by force of attraction due to gravity
∴ F = m(v^2)/r = GMm/(r^2)
∴ v = √(GM/r)

28
Q

What is the relationship between the orbital speed and orbital radius of a satellite

A

v ∝ 1/√r

∴ The larger the radius, the slower the satellite will travel

29
Q

What is the equation for the orbital period of a satellite

A

T = √(4(π^2)(r^3)/GM)

Speed = d/t (d=2πr, t=T)
∴ T = 2πr/v
v = √(GM/r)
∴ T√(GM/r) = 2πr
∴ (T^2)(GM/r) = 4(π^2)(r^2)
∴ T = √(4(π^2)(r^3)/GM)

30
Q

What is the relationship between The orbital period and orbital radius of a satellite

A

T^2 ∝ r^3

∴ The larger the radius, slower the satellite will travel, so it will take longer to complete each orbit

31
Q

What is the total energy of a satelite

A

Ek + GPE
Always remains constant

32
Q

How does the total energy of a satellite remain constant in a circular orbit

A

The orbital speed and radius are both constant
∴ Ek and GPE are both constant
∴ Total energy remains constant

33
Q

How does the total energy of a satellite remain constant in an elliptical orbit

A

As the orbital radius decreases, the speed will increase
(as v ∝ 1/√r)
∴ Ek increases as GPE decrease (and vice versa)
∴ Total energy remains constant

34
Q

What is the escape velocity of a gravitational

A

The minimum speed an unpowered object needs to completely leave the gravitational field of a planet and not ‘fall’ back towards it due to gravitational attraction

35
Q

What is the equation for the escape velocity of a gravitational field

A

v = √(2GM)/r

GPE at infinity (escape) = 0
∴ To escape the gravitational field:
loss of Ek = Gain in GPE (form negative close to surface)
∴ (1/2)mv^2 = GMm/r
∴ v = √(2GM)/r

36
Q

What is a synchronous orbit

A

When the satellite has an orbital period equal to the rotational period of the object it is orbiting
(eg. Geostationary orbit)

37
Q

What is a geostationary orbit

A

A type of synchronous orbit where the satellite always stays at the same point above the earth as it spins
- T = 24hrs
- r = 42000km (36,000km above the surface)
- Used for TV/communications

38
Q

What is a low orbit satellite

A

Any satellite orbiting between 180 and 2000km above the surface
- Orbits over north and south poles
- Used for mapping, spying, weather, etc.

39
Q

What are the benefits of Low orbit satellites

A
  • Cheaper to launch
  • Sees more detail on surface
  • More satellites available for each task
  • Needs less powerful transmitters
40
Q

What is an electric field

A

The region around a charged object where it can attract or repel other charges
(opposite charges attract and like charges repel)

41
Q

When are electric fields uniform

A

Between two parallel plates of opposite charges

42
Q

How can uniform fields be used to determine the charge of a particle within them

A
  • As a charged particle enters a uniform field (at 90 degrees), it feels a constant force parallel to the field lines
  • The direction of the force depends on the charge of the particle
  • The particle will move in a parabolic path, accelerating towards the oppositely charged plate
43
Q

When are electric fields radial

A

Around point charges

44
Q

What is the direction of an electric field (and ∴ the field lines)

A

+ → -

45
Q

How can 2D electric field lines be mapped

A

Conducting paper:
- Paper connected in series circuit, and parallel voltmeter used to measure the pd across it
- Points on the paper with the same pd can be connected to show equipotentials
- Field lines can be drawn, perpendicular to the equipotentials

46
Q

How can 3D electric field lines be mapped

A

Electrolytic tank:
- water tank placed in series circuit, containing dissolved ions (electrodes placed in tank)
- Parallel voltmeter used to find places in the water with the same pd
- Equipotentials, and therefore parallel field lines can be determined

47
Q

What is Coulomb’s law

A

F = Qq/(4πεo(r^2))

F: Magnitude of the force (Negative for attractive force, positive for repulsive force)
εo : Permittivity of free space (8.85x10^-12)
(If not in air, substituted for ε of the material)
Q & q: The charges of the 2 points
r: The distance between the two points

48
Q

What is the constant of Coulomb’s Law

A

1 / 4πεo

49
Q

What is the permittivity of free space (εo)

A

8.85x10^-12 (Fm^-1)

50
Q

Why can coulomb’s Law be described as an inverse square law

A

F ∝ 1/(r^2)
∴ The force becomes weaker at a greater distance

This is because Electric fields are radial:
- If a sphere is drawn around the point charge, radius r, all points on the sphere will experience the same force
- SA = 4π(r^2)
- ∴ x2 Radius, SA = 4π((2r)^2) = 4(4π(r^2))
- This means the surface area of the sphere increases by the square of the scale of the increase in r (SA ∝ r^2)
- The force ∝ 1/SA (field lines spread out)
- ∴F ∝ 1/(r^2)

51
Q

What is the electric field strength (E)

A

The force per unit positive charge experienced by an object in the electric field

52
Q

What is the equation for electric field strength in a uniform field

A

E = F/Q ΔV/d
(d=distance between charged plates)
(Force is a vector, pointing towards the positive charge, and is Constant in uniform fields)

53
Q

What is the equation for electric field strength in a radial field

A

E = Q/(4πεo(r^2)) = ΔV/Δr
∴ Depends on the distance from the point charge

(Derived by dividing the force from Coulomb’s Law by q)

54
Q

What is shown by the area under a graph of electric field strength against radius

A

Electric potential

55
Q

What is electric potential (V)

A

The energy required to move a unit positive charge from infinity, to a point within the field.
(Jkg^-1)

56
Q

What is absolute electric potential (V)

A

The electric potential energy that a unit positive charge would have at a certain point in the field

57
Q

When is electric potential positive or negative

A

Electric potential at infinity = 0
∴ Negative for attractive forces (-Q)
∴ Positive for repulsive forces (+Q)

58
Q

What is the equation for electric potential (in a radial field)

A

V = Q/(4πεor)

Energy to move the unit positive charge is equal to the work done
Work done = Force x distance
F = E = Q/(4πεo(r^2))
(q = 1, for unit positive charge)
d = r
∴ Er = (Q/(4πεo(r^2)))r
∴ W = Q/(4πεor)
∴ V = Q/(4πεor)

59
Q

What is shown by the gradient of a graph of electric potential against radius

A

Gradient = E
(ΔV/Δr = E)

60
Q

What is electric potential difference

A

The energy needed to move a unit positive charge between two points at different distances r from Q, in an electric field.

61
Q

What is the equation for the electric potential difference (in a radial field)

A

ΔV = Q/(4πεoΔr) = ΔV2-ΔV1

Potential difference = initial potential - final potential
∴ ΔV = ΔV2-ΔV1
∴ ΔV = Q/(4πεoΔr)

62
Q

What is the equation for work done in an electric field

A

ΔW = qΔV
(change in electric potential energy)

Work done = Force x distance
F = Qq/(4πεo(r^2))
d = Δr
∴ Fd = (Qq/(4πεo(r^2)))r
∴ ΔW = Qq/(4πεor)
ΔV = Q/(4πεoΔr)
∴ ΔW = qΔV

63
Q

What is electric potential energy

A

The energy required to move a charge q from infinity, to a point within the field. (Electric potential of charge q)

64
Q

What is the equation for the electric potential energy (in a radial field)

A

Ep = Qq/(4πεor)

Work done = qΔV
Energy required is equal to the work done
∴ Ep = qΔV
ΔV = Q/(4πεoΔr)
∴ Ep = Qq/(4πεor)

65
Q

What is the equation for the electric potential energy (in a uniform field, between 2 parallel plate)

A

Ep = Work done to move between the plates

ΔW = qΔV

66
Q

What are the main difference between gravitational and electric fields

A
  • G-fields are always attractive, whereas e-fields can be attractive or repulsive depending on the charges
  • At a subatomic level, g gravity can be ignored (due to small masses and distances), whereas e-fields are still important, as electrostatic forces are stronger than gravitational forces at these distances (electrostatic force counteracted by strong nuclear force)

Physics (14 decks)

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