Gravitational and Electric Fields Flashcards
What is a gravitational field?
A force field where any object with mass will experience an attractive force
What is a point mass?
A mass with negligible volume, or a uniform sphere whose mass acts as if it’s concentrated at the centre
What is the law of gravitation?
- An inverse square law
- Force is proportional to the inverse of distance between two point masses squared
Define gravitational field strength
The force per unit mass, in N/Kg
What is the approximate value of g on Earth?
9.81N/kg
Describe the graph of g against r for Earth
- Exponential when x = Re, where Re is the surface of the Earth
- Exponential where g = 9.81N/kg
- L shaped
Define gravitational potential
The gravitational potential energy that a unit mass would have at a specific point
Why is gravitational potential negative?
As work is being done against the gravitational field to move an object out of it
Describe the graph of V against r
- x axis(r) at the top, y axis(V) negative to zero
- Exponential when x = The radius of the sphere
- r shaped curve
What is gravitational potential difference?
The energy needed to move a unit mass
Derive the equation for gravitational potential energy
- ∆W = m ∆V
- ∆Potential energy = m ∆V
- Potential energy = m(-GM/r) = -GMm/r
What are equipotentials?
Lines(in 2D) or surface(in 3D) that join all the points with the same gravitational potential
- This means ΔV = 0 and as ΔW = mΔV, work done is also 0
What is a satellite?
Any smaller mass which orbits a much larger mass
How are satellites kept in orbit?
By the gravitational pull of the mass they’re orbiting
Derive the equation for the orbital speed of a satellite
- F = mv²/r and F = GMm/r
- mv²/r = GMm/r
- v² = GM/r
- v = √GM/r
What is the relationship between orbital speed and orbital radius of a satellite?
- Orbital speed is inversely proportional to the square root of orbital radius
- v = √GM/r
- v = √1/r
What is the orbital period?
The time taken for a satellite to complete one orbit
Derive the equation for the orbital period of a satellite
- s = d/t , so v = 2πr/T
- T = 2πr/v = 2πr/√GM/r
- T = 2πr√r/√GM
- T² = 4π²r³/GM
What is the relationship between orbital period and orbital radius of a satellite?
Orbital period squared is proportional to the orbital radius cubed
What is the on the y-axis and x-axis of a graph on orbital period?
- y axis: Period, in years
- x axis: orbital radius, in
x10⁶ m
How would kinetic and potential energies change for a satellite in an elliptical orbit?
- As the radius decreases, satellite speeds up, increasing kinetic energy and decreasing potential energy
- Total of kinetic and potential energy is always constant
Define escape velocity
The minimum speed an unpowered object to leave the gravitational field of a planet and not be pulled back due to gravitational attraction
What principle is used to derive the escape velocity equation, stating the formula based on the principle?
- Conservation of energy
- Kinetic energy lost = Gravitational potential energy gained
Derive the escape velocity equation
- KE = 1/2mv² and GPE = GMm/r
- 1/2mv² = GMm/r
- 1/2v² = GM/r
- v² = 2GM/r
- v = √2GM/r
What is a synchronous orbit?
An object has a orbital period equal to the rotational period of the object it’s orbiting
What are geostationary satellites?
An Earth satellite that orbits directly over the equator and is always above the same point of Earth
Define low orbiting satellites
Satellites which orbit between 180km-2000km above Earth
State the advantages and a disadvantage of low orbiting satellites
Advantages:
- Cheaper to launch
- Require less powerful transmitters as closer
Disadvantage:
- Proximity to Earth and high orbital speeds mean multiple satellites working together are needed for constant coverage
State 3 applications of low orbiting satellites
- Communications
- Mapping
- Monitoring weather
What are point charges?
A charge with negligible volume, or a uniform sphere whose charge acts as if it’s concentrated at the centre
State Coulomb’s Law
F = kQq/r² , where k = 1/4πε0 , ε0 = permittivity of free space in F/m
State the relationship the force on the object has with the distance between charges?
- Inverse square law
- Force is proportional to the inverse of the distance between charges squared
Define electric field strength, E
Force per unit positive charge
What are electric field lines?
Lines that show the direction of the force that would act on a charge
Which way do electric field lines point for positive and negative point charges?
- Lines point outward for a positive point charge
- Lines point inward for a negative point charge
Which way do the lines point between two parallel plates?
From the higher voltage plate to lower voltage plate
What surrounds a point charge?
A radial field
What is the relationship between electric field strength and distance from the point charge?
- Inverse square law
- Electric field strength is proportion to the inverse of the distance from the point charge squared
If a point charge is no longer used, does the inverse square law still apply to the radial field?
No, electric field strength will not be proportional to the inverse of the distance from the charge
Describe the graph of Electric field strength against r for a point charge
- E decreases in a curve as r increases
- For a point charge, E becomes infinitely large as r tends to 0
Describe the graph of Electric field strength against r for a charged sphere
- Exponential on the x-axis at Rs, where Rs = sphere radius
- Exponential on the y-axis at Es where Es = Electric field strength at surface of sphere
- E decreases from the exponentials as r increases
How can a uniform field be produced?
By connecting two parallel plates to the opposite poles of a battery
How can you determine if a particle has charge?
- By putting the particle in a uniform field
- A positive particle that enters at right angles to the field lines will have its force in the same direction as the field lines
- A negative particle that enters at right angles to the field lines will have its force in the opposite direction of the field lines
- Particle accelerates at right angles and follows a curved path in either direction
Define absolute electric potential
The electric potential energy a unit positive charge would have at that point
State the equation for absolute electric potential
V = kQ/r, where k = 1/4πε0
Describe the graph for V against r for a positive charge
- Graph curving in an l shape
- As r increases, V decreases
Describe the graph for V against r for a negative charge
- Max value of V = 0
- x axis on the top
- Graph curving in an r shape
What does the gradient of a tangent for a V against r graph for a positive or negative charge give?
The electric field strength, E = ΔV/Δr
What is electric potential difference?
The difference between the absolute electric potential of two points within an electric field
What does the area under an E against r graph give?
Change in electric potential
How is the area under a E against r graph calculated?
By counting the squares of the area to be found
What is the equation for energy needed to move a charge across a potential difference?
ΔW = QΔV
Derive the equation for the energy needed to move charge across a potential difference
E = ΔV/d = F/Q
- ΔV/d = F/Q
- QΔV = Fd and as W = Fd, for a moving charge:
- QΔV = ΔW
What is the main difference between gravitational fields and electric fields?
Gravitational fields can only be attractive whereas electric fields can be attractive and repulsive
Which one of these forces can be ignored at a subatomic level and why?
Gravitational force as despite being close together, all the particles have incredibly small mass
Where is the gravitational potential energy stored?
In the gravitational field, between the masses
Where is electrical potential energy stored?
In the electric field, between the charges
