Section 9 - Gravitational and Electric Fields Flashcards
What is a force field?
A region where an object will experience a non-contact force.
What do force fields cause?
Interactions between objects or particles.
What is a gravitational field?
A region where objects with mass will experience an attractive force.
How can a force field be represented?
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.
How are field lines used to show the strength of a field?
The further apart the lines are, the weaker the field.
Describe the gravitational field of the Earth.
- 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
Practice drawing out the Earth’s gravitational field.
See diagram pg 120 of revision guide.
What is Newton’s Law of Gravitation?
- An equation used to calculate the gravitational force between two point masses
- F = Gm₁m₂ / r²
What is the equation for the gravitational force between two point masses (Newton’s Law of Gravitation)?
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)
What type of law is Newton’s Law of Gravitation and how can this be symbolised?
- Inverse square law
* F ∝ 1 / r²
If the distance between 2 point masses is doubled, what happens to the magnitude of the gravitational force between them?
It is one quarter of the original.
What has a bigger impact on the size of the gravitational force, the distance between them or the mass?
- The distance
* This can be seen with Newton’s Law of Gravitation
In gravitational calculations, what is G?
- The gravitational constant
- It is used in some equations
- 6.67 x 10^-11 Nm²/kg²
What is gravitational field strength?
• The force per unit mass exerted at a given position in a gravitational field.
OR
• The acceleration of a mass in a gravitational field.
What is the symbol for gravitational field strength?
g
What are the units for gravitational field strength?
N/kg or m/s²
What is the equation that defines gravitational field strength?
g = F / m
Where:
• g = Gravitational field strength (N/kg)
• F = Force (N)
• m = Mass (kg)
Is the value of g constant throughout a field?
No, its value depends on the where you are in the field.
What is the value of g at the Earth’s surface?
9.81 N/kg (or m/s²)
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.
In a radial field, how does g vary with the radius from the centre of the mass?
g is inversely proportional to r²
Describe the gravitational field around a point mass.
Radial
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)
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)
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
(See diagram pg 121 of revision guide)
Remember to practise drawing out the graph of g against r for a point mass.
See diagram of 121 of revision guide.
What is gravitational potential?
The gravitational potential energy that a unit mass would have at that point in a gravitational field.
What is the symbol for gravitational potential?
V
What are the units for gravitational potential?
J/kg
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
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)
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
Which quantities in gravitational field questions are always negative?
- Gravitational potential
* Gravitational potential energy (GPE)
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
At infinite distance from a planet, what is the gravitational potential and GPE?
- Gravitational potential (0J/kg)
* GPE (0J)
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
(See diagram pg 122 of revision guide)
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
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
(See diagram pg 122 of revision guide)
How do you work out ΔV using a g-r graph?
- Area under the curve between two x-values
* Because -ΔV = g x Δr
Remember to practise drawing out all 3 gravitational field graphs. Also, practise finding different quantities from them.
Pgs 121 + 122 of revision guide
What is escape velocity?
- The velocity at which an object’s kinetic energy is equal to minus its gravitational potential energy
- It is the velocity at which an object must travel in order to escape a gravitational field
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)
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.
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)
What is the equation for GPE relative to G, M and r?
GPE = -GMm/r
This is derived from V = -GM/r
Is escape velocity dependent on the mass of the object?
No, it is the same for all masses in a gravitational field.
What is gravitational potential difference?
The energy needed to move a unit mass between two gravity sonar potentials.
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)
What are equipotentials?
Lines (in 2D) or surfaces (in 3D) that join all of the points with the same potential (V).
How much work is done when moving an object along an equipotential?
0J
Describe the equipotentials around a uniform spherical mass.
Spherical surfaces
Describe how equipotentials and field lines are related in gravitational fields.
They are perpendicular.
What force keeps an object undergoing circular motion in orbit?
Centripetal force
In the case of a satellite orbiting the Earth, what is the centripetal force?
Gravitational force
Give the relationship between the time period and radius of an orbit.
• T² = 4π²r³ / GM
So
• T² ∝ r³
(NOTE: Not given in exam)
Derive the relationship between the period and radius of an orbit.
• 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
How is the speed of a satellite related to its orbital radius?
• v = √(GM / r)
So:
• v ∝ 1 / √r
(NOTE: This comes from the first part of the T² ∝ r³ derivation.)
Remember to practise deriving the relationship between T and r for a satellite.
Pg 124 of revision guide
If T² ∝ r³, what can be said to be constant?
T² / r³ = Constant
Do the practise question on pg 124 of revision guide.
Do it.
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.
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
Why is a satellite’s energy constant in elliptical orbit?
- The satellite speeds up as it’s height decreases and slows down as height increases
- So kinetic energy increases as potential energy decreases (and vice versa)
- So the total energy remains constant
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.
What is a synchronous orbit?
Where the orbital period is the same as the rotational period of the orbited object.
What are the two types of satellite?
- Geostationary
* Low orbit
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.
Describe the orbit that geostationary satellites have.
Synchronous, along the equator.
What is the time period of orbit of a geostationary satellite?
1 day
What is the orbital radius of a geostationary satellite?
42,000km (about 36,000km above the Earth’s surface)
What are geostationary satellites used for?
Sending TV and telephone signals.
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.
Describe the orbit that low-orbit satellites have.
Usually in a plane that includes the north and south pole.
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
At what height do low orbit satellites orbit?
180-2000km above the surface
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
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
Does any charged object have an electric field around it?
Yes
What is an electric field?
A region where charged objects will experience a non-contact force.
What is the unit for electric charge?
Coulombs (C)
What is the symbol for electric charge?
Q
Can charge be positive and negative?
Yes
Oppositely charged particles…
Attract
Like charges…
Repel
What happens when a charged object is placed in an electric field?
It experiences a force.
In electric field questions, what can he assumed about a charged object that is a sphere?
All of its charge is at its centre.
How can electric fields be represented?
Using field lines.
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
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)
What type of law is Coulomb’s law?
- Inverse square law
* Since F ∝ 1/r²
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
What is electric field strength?
The force per unit positive charge exerted at a certain point in an electric field.
What is the symbol for electric field strength?
E
What is the unit for electric field strength?
N/C
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)
Is electric field strength a scalar or vector quantity?
Vector
Is electric field strength a constant?
No, it depends on where you are in the electric field (unless it is uniform).
What type of electric field does a point charge have?
Radial field
Remember to revise the field line diagrams on the bottom of pg 126 of revision guide.
Do it.
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
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
What happens to the field lines as you get further away from a point charge?
They get further apart.
Describe the graph for E against r for an electric field around a point charge.
1/x² graph.
See diagram pg 127 of revision guide
How can a uniform electric field be produced?
Connecting two parallel plates to opposite poles of a battery.
What can be said about electric field strength in a uniform electric field?
It is the same at all points.
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 between plates (V)
• d = Distance between plates (m)
What is an alternative unit for electric field strength in a uniform field?
V/m
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
What is a particle’s curved path in an electric field called?
Parabola
What is absolute electric potential?
The electric potential energy that a unit positive charge would have at a point in an electric field.
What is the symbol for electric potential?
V
What are the units for electric potential?
Volts (V)
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
When is V positive around a point charge?
When Q is positive.
When is V negative around a point charge?
When Q is negative.
When is the magnitude of the electric potential around a point charge the greatest?
On the surface of the charge.
What is electric potential (V) equal to at infinite distance?
0V
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.
(See diagram pg 128 of revision guide)
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.
(See diagram pg 128 of revision guide)
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)
How can electric field strength be found from a V-r graph around a point charge?
- Gradient
* Because E = ΔV / Δr
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
What is electric potential difference?
The energy needed to move a unit positive(?) charge between two points.
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)
What is the symbol for electric potential difference?
ΔV
Derive the formula for work done in moving a charge through an electric potential difference.
- E = F / Q = ΔV / d
- Fd = QΔV
- ΔW = QΔV
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)
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
What are equipotentials in electric fields?
Lines that show all points of equal potential in the electric field.
What shape are equipotentials around a point charge?
Spherical
Describe what equipotentials look like between parallels plates (in a uniform electric field).
They are parallel to each plate, with equal spacing.
Remember to practise drawing out equipotentials around a point charge or between two parallel plates.
Pg 129 of revision guide
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
Describe how the electric and gravitational field equations differ.
- Q is used instead of m (or M)
* 1/4πε₀ is used instead of G
Remember to practise listing all the similarities between electric and gravitational fields.
Pg 130 of revision guide
What is the one important difference between electric and gravitational fields?
Gravitational fields are always attractive, whereas electric forces can be attractive or repulsive.
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
