Section 9 - Gravitational and Electric Fields Flashcards
1
Q
What is a force field?
A
A region where an object will experience a non-contact force.
2
Q
What do force fields cause?
A
Interactions between objects or particles.
3
Q
What is a gravitational field?
A
A region where objects with mass will experience an attractive force.
4
Q
How can a force field be represented?
A
Using field lines (or “lines of force”) that show the direction of the force that would be exerted on an object in a given position.
5
Q
How are field lines used to show the strength of a field?
A
The further apart the lines are, the weaker the field.
6
Q
Describe the gravitational field of the Earth.
A
- It is radial, so the field lines meet at the centre of the Earth like a spiderweb
- Close to the surface, the field can be considered almost uniform since the field lines are almost parallel and equally spaced
7
Q
What does Earths radial field look like?
A
8
Q
What is Newton’s Law of Gravitation?
A
- An equation used to calculate the gravitational force between two point masses
- F = Gm₁m₂ / r²
9
Q
What will the force experienced by an object in a gravitational field always be?
A
Attractive
10
Q
What is the equation for the gravitational force between two point masses (Newton’s Law of Gravitation)?
A
F = Gm₁m₂ / r²
Where:
• F = Force (N)
• G = Gravitational constant = 6.67 x 10^-11 Nm²/kg²
• m = Mass (kg)
• r = Distance between centres of two point masses (m)
11
Q
Where do we assume all the weight is concentrated for objects that experience a force?
A
In the centre - e.g. uniform spheres
12
Q
When talking about a mass of an object in orbit, what is M (or M1) and what is m (or M2)
A
M = mass of larger object m = mass of smaller, orbiting object
13
Q
How do you get the equation for speed of an object orbiting a larger object (e.g. a planet)?
A
GMm/r^2 = mv^2/r.
The smalls m’s cancel and one of the r’s cancel.
V = squareroot(GM/r)
14
Q
What is the equation of the time period of earths orbit?
A
Time = distance/speed.
T = 2πr/v
15
Q
What type of law is Newton’s Law of Gravitation and how can this be symbolised?
A
- Inverse square law
* F ∝ 1 / r²
16
Q
If the distance between 2 point masses is doubled, what happens to the magnitude of the gravitational force between them?
A
It is one quarter of the original.
17
Q
What has a bigger impact on the size of the gravitational force, the distance between them or the mass?
A
- The distance
* This can be seen with Newton’s Law of Gravitation
18
Q
In gravitational calculations, what is G?
A
- The gravitational constant
- It is used in some equations
- 6.67 x 10^-11 Nm²/kg²
19
Q
What is gravitational field strength?
A
• The force per unit mass exerted at a given position in a gravitational field.
OR
• The acceleration of a mass in a gravitational field.
20
Q
What is the symbol for gravitational field strength?
A
g
21
Q
What are the units for gravitational field strength?
A
N/kg or m/s²
22
Q
What is the equation that defines gravitational field strength?
A
g = F / m
Where:
• g = Gravitational field strength (N/kg)
• F = Force (N)
• m = Mass (kg)
23
Q
Is the value of g constant throughout a field?
A
No, its value depends on the where you are in the field.
24
Q
What is the value of g at the Earth’s surface?
A
9.81 N/kg (or m/s²)
25
Because F is a vector, where is the direction of the force always towards? (common sense)
Towards the the centre of the mass which caused the gravitational force
26
Is g constant around the world?
The gravitational field is almost uniform at the Earth’s surface, so you can assume that g is a constant as long as you don’t go too high above the Earth’s surface.
27
The force on M1 due to M2 to equal and opposite to the force on...
M2 due to M1
28
In a radial field, how does g vary with the radius from the centre of the mass?
g is inversely proportional to r²
29
When we (humans) fall to the ground, why don't we notice Earth's acceleration towards us?
30
Describe the gravitational field around a point mass.
Radial
31
Give the equation for g around a point mass.
g = GM / r²
OR
g = -ΔV / Δr
```
Where:
• g = Gravitational field strength (N/kg)
• G = Gravitational constant (Nm²/kg²)
• M = Point mass (kg)
• r = Distance from centre (m)
• V = Gravitational potential (J/kg)
```
32
What kind of law is the equation that gives g relative to the distance from a point mass?
Inverse square law (since g is inversely proportional to r²)
33
Describe the graph of g against r for a point mass.
* Does not cross y-axis
* Curve starts at its highest point at a certain x-value (RE - radius of the Earth)
* It then curves like a 1/x² graph and never quite reaches the x-axis
34
Remember to practise drawing out the graph of g against r for a point mass.
See diagram of 121 of revision guide.
35
What is gravitational potential?
The gravitational potential energy that a unit mass would have at that point in a gravitational field.
36
What is the symbol for gravitational potential?
V
37
What is the equation for gravitational field strength with F and M?
g = F/M
38
What are the units for gravitational potential?
J/kg
39
g= F/M, what is the F?
Force experienced by a mass in the field
40
What is the difference between gravitational potential energy and gravitational potential?
* Gravitational potential -> GPE that a unit mass would have at a given point in a gravitational field
* Gravitational potential energy -> The energy that a mass has due to its position in a gravitational field
41
Why do we assume g is constant
Almost uniform field near earth's surface
42
What is the equation for gravitational potential?
V = -GM / r
Where:
• V = Gravitational potential (J/kg)
• G = Gravitational constant = 6.67 x 10^-11 Nm²/kg²
• M = Mass of point mass (kg)
• r = Distance from centre of point mass (m)
43
What is unusual about gravitational potential and GPE? Why?
* They are negative, since you can think of it of as negative energy since work has to be done to move an object out of the field
* They becomes less negative with distance from the point mass
* At infinite distance, the gravitational potential is 0J/kg and GPE is 0J
44
Which quantities in gravitational field questions are always negative?
* Gravitational potential
| * Gravitational potential energy (GPE)
45
How is g = GM / r² derived?
46
Describe how gravitational potential (and GPE) changes with distance from a planet’s surface.
* Most negative on the planet’s surface
* Becomes less negative with distance from the planet
* 0J/kg at infinite distance
47
At infinite distance from a planet, what is the gravitational potential and GPE?
* Gravitational potential (0J/kg)
| * GPE (0J)
48
Describe a graph of V against r for the Earth.
* Does not cross y-axis
* Curve starts at its most negative point at a certain x-value (RE - radius of the Earth)
* It then curves like a -1/x graph and never quite reaches the x-axis
49
Because Gravitational fields are vectors, what can you do to them?
add up to find combined effect of more than 1 object
50
How can you work out the value of g at a certain point using a V-r graph for a point mass?
* Find the gradient at any point
| * This is because g = -ΔV / Δr
51
52
Describe a graph of g against r for the Earth.
* Does not cross y-axis
* Curve starts at its highest point at a certain x-value (RE - radius of the Earth)
* It then curves like a 1/x graph and never quite reaches the x-axis
53
How do you work out ΔV using a g-r graph?
* Area under the curve between two x-values
| * Because -ΔV = g x Δr
54
Remember to practise drawing out all 3 gravitational field graphs. Also, practise finding different quantities from them.
Pgs 121 + 122 of revision guide
55
What is escape velocity?
* The velocity at which an object’s kinetic energy is equal to minus its gravitational potential energy
* It is the minimum velocity at which an object must travel in order to escape a gravitational field
56
Why is potential negative?
Have to do work against the field to move an object out of it.
57
What is an object’s total energy when it travels at escape velocity?
* Zero
| * Because the kinetic energy and GPE sum to 0 (since GPE is always negative)
58
What is the equation for escape velocity?
v = √(2GM/r)
Where:
• v = Escape velocity (ms⁻²)
• G = Gravitational constant = 6.67 x 10^-11 Nm²/kg²
• M = Mass of point mass (kg)
• r = Distance from centre of point mass (m)
NOTE: Not given in exam.
59
Derive the equation for escape velocity.
* KE = 1/2mv²
* GPE = -GMm/r
* 1/2mv² = GMm/r
* 1/2v² = GM/r
* v² = 2GM/r
* v = √(2GM/r)
60
What is the equation for GPE relative to G, M and r instead of mgh?
GPE = -GMm/r
| This is derived from V = -GM/r
61
How do you derive GPE = -GMm/r
Work done = m x V.
V = -GM/r
replace V with mV (which is work done) =
mV = -GMm/r, which is
GPE = -GMm/r
62
How do you find the change in kinetic energy of a satellite when it moves from and orbit of R1 to a lower orbit of R2?
(GPE lost = KE gained).
v = √(GM / r).
KE = 1/2 mv^2.
KE = 1/2 m(√(GM / r))^2
KE = GMm/2r
Change in KE = GMm/2(R1) - GMm/2(R2)
63
Is escape velocity dependent on the mass of the object?
No, it is the same for all masses in a gravitational field.
64
What is gravitational potential difference?
The energy needed to move a unit mass between two gravity sonar potentials.
65
What is the equation for the work done when moving an object through a gravitational potential difference?
ΔW = mΔV
Where:
• ΔW = Work fine (J)
• m = Mass (kg)
• ΔV = Gravitational potential difference (J/kg)
66
What are equipotentials?
Lines (in 2D) or surfaces (in 3D) that join all of the points with the same potential (V).
If you travel along an equipotential, your potential doesn't change.
67
How much work is done when moving an object along an equipotential?
0J
Change in potential = 0
Change in work done = Mass x change in potential.
68
Describe the equipotential around a uniform spherical mass.
Spherical surfaces
69
Describe how equipotential and field lines are related in gravitational fields.
They are perpendicular.
70
What force keeps an object undergoing circular motion in orbit?
Centripetal force
71
In the case of a satellite orbiting the Earth, what is the centripetal force?
Gravitational force.
| They are kept in orbit by the gravitational "pull" of of the mass (Earth) they orbit.
72
Give the relationship between the time period and radius of an orbit.
• T² = 4π²r³ / GM
So
• T² ∝ r³
(NOTE: Not given in exam)
73
Derive the relationship between the period and radius of an orbit.
Find two equations with force and velocity and find velocity, v.
Then use the time period equation to change v into T:
```
• Centripetal force:
F = mv² / r
• Attraction due to gravity:
F = GMm / r²
• mv² / r = GMm / r²
• v² = GMmr / r²m
• v = √(GM / r)
• Since one orbit is 2πr:
v = 2πr / T
• T = 2πr / v
• T = 2πr / √(GM / r)
• T = 2πr√r / √(GM)
• T² = 4π²r³ / GM
• Therefore:
T² ∝ r³
```
74
How is the speed of a satellite related to its orbital radius?
• v = √(GM / r)
So:
• v ∝ 1 / √r
So greater radius = lower speed
(NOTE: This comes from the first part of the T² ∝ r³ derivation.)
75
Remember to practise deriving the relationship between T and r for a satellite.
Pg 124 of revision guide
76
If T² ∝ r³, what can be said to be constant?
T² / r³ = Constant
77
78
What can be said about the energy of an orbiting satellite?
It is constant, since the kinetic and potential energy always sum to a constant value.
79
How can this equation: ΔW = mΔV, be used for potential energy, then how can you make it become: GPE = -GMm/r ?
80
Why is a satellite’s energy constant in circular orbit?
* Speed and distance above the Earth do not change
* So the kinetic energy and potential energy are constant
* So the total energy is always constant
81
Why is a satellite’s energy constant in elliptical orbit?
* The satellite speeds up as it’s orbital radius decreases and slows down as orbital radius increases
* So kinetic energy increases as potential energy decreases (and vice versa)
* So the total energy remains constant
82
What is it important to remember about r?
It is measured from the centre of the orbit (or the centre of the point mass), not the surface of the Earth.
83
What is a synchronous orbit?
Where the orbital period is the same as the rotational period of the orbited object.
84
What are the two types of satellite?
* Geostationary
| * Low orbit
85
What are geostationary satellites?
Satellites that have the same angular speed as the Earth turns below them, so that they stay in the same position above the Earth.
86
Describe the orbit that geostationary satellites have.
Synchronous, along the equator.
87
What is the time period of orbit of a geostationary satellite?
1 day
88
What is the orbital radius of a geostationary satellite?
42,000km (about 36,000km above the Earth’s surface)
89
What are geostationary satellites used for?
Sending TV and telephone signals.
90
What are low orbit satellites?
Satellites that orbit between 180-2000km above the Earth, so that they do not stay in the same place relative to the Earth.
91
Describe the orbit that low-orbit satellites have.
Usually in a plane that includes the north and south pole.
92
Compare the advantages of low orbit satellites and geostationary satellites.
Low orbit
• Cheaper to launch
• Require less powerful transmitters since they are close to Earth
Geostationary
• Do not require multiple satellites to achieve constant reception in one area
93
How is T against r plotted?
Logarithmic scale:
94
At what height do low orbit satellites orbit?
180-2000km above the surface
95
What are low orbit satellites used for?
* Communications -> Cheap to launch and do not require powerful transmitters, although many are required for constant coverage
* Imaging and weather -> Due to being close enough to see surface in high detail
96
What type of satellite can be used to monitor the whole Earth and why?
* Low orbit satellites
| * Each orbit is over a different part of the Earth’s surface as the Earth rotates underneath
97
Where does a satellite orbit for an elliptical orbit?
98
What kind of satellite is the ISS?
Low orbiting
99
State 2 reasons why rockets launched from the Earth's surface do not need to achieve escape velocity to reach their orbit?
They don't need to escape gravitational field, only need to reach the orbit = less energy required.
Energy is added during the flight (with fuel) providing a continuous thrust.
100
Does any charged object have an electric field around it?
Yes
101
What is an electric field?
A region where charged objects will experience a non-contact force.
102
What is the unit for electric charge?
Coulombs (C)
103
What is the symbol for electric charge?
Q
104
Can charge be positive and negative?
Yes
105
Oppositely charged particles...
Attract
106
Like charges...
Repel
107
What happens when a charged object is placed in an electric field?
It experiences a force.
108
In electric field questions, what can he assumed about a charged object that is a sphere?
All of its charge is at its centre.
109
How can electric fields be represented?
Using field lines.
110
State Coulomb’s law.
* The magnitude of the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
* F = 1/4πε₀ x Q₁Q₂/r²
111
Give the equation for Coulomb’s law.
F = 1/4πε₀ x Q₁Q₂/r²
```
Where:
• F = Force (N)
• ε₀ = Permittivity of free space = 8.85 x 10^-12 F/m
• Q = Charge (C)
• r = Distance between charges (m)
```
112
What type of law is Coulomb’s law?
* Inverse square law
| * Since F ∝ 1/r²
113
What is the significance of the ε in Coulomb’s law?
* This is the permittivity of the material the charges are in
* This affects the size of the force between the charges
* If the system is in air, it can be considered the same as in a vacuum
114
What is electric field strength?
The force per unit *positive* charge exerted at a certain point in an electric field.
115
What is the symbol for electric field strength?
E
116
What is the unit for electric field strength?
N/C
117
What is the equation than defines electric field strength?
E = F/Q
Where:
• E = Electric Field Strength (N/C)
• F = Force (N)
• Q = Charge (C)
118
Is electric field strength a scalar or vector quantity?
Vector
119
Is electric field strength a constant?
No, it depends on where you are in the electric field (unless it is uniform).
120
What type of electric field does a point charge have?
Radial field
121
For 2 positive parallel plates, which way do the field lines point?
From the plate with more positive voltage to the plate with less positive voltage.
122
How can you measure electric field lines?
123
What does a field line diagram look like?
124
Give the equation for the electric field strength around a point charge.
E = 1/4πε₀ x Q/r²
```
Where:
• E = Electric field strength (N/C)
• ε₀ = Permittivity of free space = 8.85 x 10^-12 F/m
• Q = Charge of point charge
• r = Distance from the point charge
```
125
What type of equation is the equation that is used to find the electric field strength around a point charge?
* Inverse square law
| * Since E ∝ 1/r²
126
What happens to the field lines as you get further away from a point charge?
They get further apart.
127
Describe the graph for E against r for an electric field around a point charge.
1/x² graph.
128
When will a charged not follow the inverse square law?
If it isn't a point charge (e.g. a metal sphere)
129
How can a uniform electric field be produced?
Connecting two parallel plates to opposite poles of a battery.
130
What can be said about electric field strength in a uniform electric field?
It is the same at all points.
131
What is the equation that defines electric field strength in a uniform electric field?
E = V/d
Where:
• E = Electric field strength (N/C or V/m)
• V = Potential difference (change) between plates (V)
• d = Distance between plates (m)
132
What is an alternative unit for electric field strength in a uniform field?
V/m
133
What can a uniform electric field be used for? How?
* Determining whether a particle is charged.
* If a particle curves in the same direction as the field lines, it is positively charged
* If a particle curves in the opposite direction as the field lines, it is negatively charged
134
What angle will a charged particle that enters an electric field feel a constant force parallel to the electric field lines?
enters the field at right angles
135
What is a particle’s curved path in an electric field called?
Parabola
136
What is absolute electric potential?
The electric potential energy that a unit *positive* charge would have at a point in an electric field.
137
What effects electric potential?
Size of charge creating the electric field and distance from the charge.
138
What is the symbol for electric potential?
V
139
What are the units for electric potential?
Volts (V)
140
Give the equation for electric potential around a point charge.
V = 1/4πε₀ x Q/r
```
Where:
• V = Electric potential (V)
• ε₀ = Permittivity of free space = 8.85 x 10^-12 F/m
• Q = Charge of point charge
• r = Distance from the point charge
```
141
When is V positive around a point charge?
When Q is positive. Force is repulsive
142
When is V negative around a point charge?
When Q is negative. Force is attractive
143
When is the magnitude of the electric potential around a point charge the greatest?
On the surface of the charge.
144
What is electric potential (V) equal to at infinite distance?
0V
145
Describe the graph of V against r around a point charge for a repulsive force.
* 1/x² graph
| * This is because a repulsive force must mean a positive point charge, so V is always positive.
146
Describe the graph of V against r around a point charge for an attractive force.
* -1/x² graph
| * This is because an attractive force must mean a negative point charge, so V is always negative.
147
What equation relates electric field strength with the change in electric potential around a point charge?
E = ΔV / Δr
Where:
• E = Electric field strength (N/C or V/m)
• ΔV = Electric potential difference (V)
• Δr = Change in distance from the charge (m)
148
How can electric field strength be found from a V-r graph around a point charge?
* Gradient of tangent
| * Because E = ΔV / Δr
149
How can potential difference between two points be found from an E-r graph around a point charge?
* Area under graph between two points
| * Because E = ΔV / Δr so ΔV = E x Δr
150
What is electric potential difference?
The energy needed to move a unit (*positive*(?)) charge between two points.
151
What equation gives the work required to move a charge through an electric potential difference?
ΔW = Q x ΔV
Where:
• ΔW = Work done (J)
• Q = Charge being moved (C)
• ΔV = Electric potential difference (V)
152
What is the symbol for electric potential difference?
ΔV
153
Derive the formula for work done in moving a charge through an electric potential difference.
* E = F / Q = ΔV / d
* Fd = QΔV
* ΔW = QΔV
154
What is the equation for the work done to move a mass through a gravitational field?
ΔW = mΔV
Where:
• ΔW = Work done (J)
• m = Mass (kg)
• ΔV = Potential difference (ΔV)
155
Derive the equation for the work done to move a mass through a gravitational field.
* g = -ΔV / Δr = F / m (since the gravitational field is considered near uniform near the Earth)
* mΔV = -FΔr
* ΔW = mΔV
156
What are equipotentials in electric fields?
Lines that show all points of equal potential in the electric field.
157
What shape are equipotentials around a point charge?
Spherical
158
Describe what equipotentials look like between parallels plates (in a uniform electric field).
They are parallel to each plate, with equal spacing.
| Right angles to field lines
159
What do equipotentials around a point charge and between two parallel plates look like?
160
What are the Inverse square laws that are seen in both electric and gravitational fields?
* Force between two masses / point charges
| * Field strength around a mass / point charge
161
Describe how the electric and gravitational field equations differ.
* Q is used instead of m (or M)
| * 1/4πε₀ is used instead of G
162
Remember to practise listing all the similarities between electric and gravitational fields.
Pg 130 of revision guide or pg 300 of revision guide
163
What is the one important difference between electric and gravitational fields?
Gravitational fields are always attractive, whereas electric forces can be attractive or repulsive.
164
At sub-atomic level, does electrostatic or gravitational force have a greater effect and why?
* Electrostatic
* Because the masses are tiny, so the gravitational force is also tiny
* NOTE: There are other forces that keep the nucleus stable
