Gravitational and Electric Fields Flashcards
What type of field is a gravitational field?
A gravitational field is a force field
What is a force field?
- A force field is a region where an object will experience a non-contact force
- Force fields cause interactions between objects or particles or in the case of gravity, between masses
What type of quantity is a force field?
A vector quantity
What happens when an object is put in the gravitational field of another object?
Any object with mass will experience an attractive force if you put it in the gravitational field of another object
How can you represent the force field around an object?
Force fields can be represented as vectors showing the direction of the force they would exert on an object placed in that field. Gravitational field lines are arrows showing the direction of the force that masses would feel in a gravitational field
How can you tell the direction of the force in a force field diagram?
The direction that the arrows are pointing in shows the direction of the force
What would happen if you put a small mass anywhere in the Earth’s gravitational field?
If you put a small mass anywhere in the Earth’s gravitational field it will always be attracted towards the Earth
What type of field is the Earth’s gravitational field?
The Earth’s gravitational field is radial - the lines of force meet at the centre of the Earth
Explain in terms of field lines the effect on the force felt by a mass in the Earth’s gravitational field if it were moved further away?
If the mass is moved further away from the Earth where the lines of force are further apart the force it experiences decreases
Why does the gravitational field of a small mass in the Earth’s gravitational field not affect the Earth?
The gravitational field of the mass does not affect the Earth as the Earth is much more massive
How is an uniform field represented on a field line diagram?
The field lines are parallel and equally spaced
Define a gravitational force field
A region in which an object with mass experiences weight
State the equation given by Newton’s Law of Gravitation and each variable
F = Gm1m2/r^2
- G is the gravitational constant
- m1 and m2 are the respective masses of the objects involved
- r is the distance between the centres of the two masses in metres
- F is the magnitude of the gravitational force between masses m1 and m2
State Newton’s Law of Gravitation
The gravitational force of attraction between two masses is inversely proportional to the distance between their centre of masses squared and is directly proportional to the product of the two masses
What would happen to the force between two objects in a gravitational field if the distance r between two masses increases?
As Newton’s law of gravitation is an inverse square law, F ∝ 1/r^2
If the distance r between the masses increases the force F will decrease
What would happen to the force between two objects in a gravitational field if the distance between them doubles?
If the distance between two objects in a gravitational field doubles then the force will be one quarter of the original force
What does the gradient of a force-mass graph tell us?
The gravitational field strength
Define gravitational field strength
The gravitational field strength at a point in a gravitational field is the force acting per unit mass at that point
What is the formula for calculating the gravitational field strength of a uniform field?
g = F/m
- F is the force experienced by a mass when its placed in a gravitational field
- Units are N/kg
What is the gravitational field strength at a point equal to?
The gravitational field strength at a point is equal to the acceleration due to gravity at the point
What type of quantity is gravitational field strength?
A vector quantity
What is the formula for calculating the gravitational field strength in a radial field and what are the variables?
- g = GM/r^2
- G is the gravitational constant
- M is a point mass (kg)
- r is the radius of the mass (m)
What type of objects have a radial field?
Spherical objects
What type of relationship does gravitational field strength and distance have?
They have an inverse square law relationship meaning that as r increases, g decreases
Draw a graph of g against r to show the inverse square law relationship between them
- See page 121 in the revision guide*
See page 7 in g fields pack
Define gravitational potential
The gravitational potential at a point is defined as the work done in bringing unit mass from infinity to that point in the gravitational field
What is the formula for calculating gravitational potential in a radial field and its variables?
V = -GM/r
- V is gravitational potential
- M is the mass of the object causing the gravitational field
- r is the distance from the centre of the object
What is the gravitational potential at an infinite distance from an object?
0
Why are GPE and gravitational potential always negative?
GPE and gravitational potential are always negative because gravity causes an attractive force and you have to do work against the gravitational field to move an object out of it
What is the formula used to calculate gravitational field strength from gravitational potential?
g = - ΔV/Δr
What is the gradient of a graph of gravitational potential against distance?
The gravitational field strength
What is the area under a graph of gravitational field strength against distance?
The change in gravitational potential
Define escape velocity
The minimum speed an unpowered object needs in order the leave the gravitational field of a planet (or star)
Derive the formula for escape velocity
See page 122 in the revision guide
1- 1/2mv^2 - GMm/r = 0
2- 1/2mv^2 = GMm/r
3 - 1/2v^2 = GM/r
4 - v^2 = 2GM/r
5 - v = √2GM/r
Define gravitational potential difference
Gravitational potential difference is the energy needed to move a unit mass
(Difference in gravitational potential between two points, not traditional pd)
What is the formula used to calculate the work done when moving an object in a gravitational field?
ΔW = mΔV
- ΔW is the work done in J
- ΔV is the gravitational potential difference
- m is the mass of the object
What are gravitational equipotentials?
Gravitational equipotentials are lines in 2D and surfaces in 3D that join all of the points with the same potential. They show all points of equal potential in a field
What happens as you travel along an equipotential in terms of energy transfer?
As you travel along an equipotential, no work is done moving along an equipotential. This means that for the journey ΔV = 0
What is the relationship between equipotentials and field lines?
Equipotentials and field lines are perpendicular
What are the differences when calculating the work done in both uniform and non-uniform fields?
- In a uniform field the gravitational field strength is constant so we can calculate work done using GPE = mgh
- In a non-uniform field the gravitational field strength is not constant so we have the calculate the work done using ΔW=mΔV
Show the relationship between the period and the radius of an orbit to be T^2∝r^3
1- The force acting on an object in circular motion is given by F=mv^2/r
2- The force of attraction due to gravity between two objects with masses is given by F=GMm/r^2
3- Make the two equations equal and rearrange to find the speed of a satellite in a gravitational field to get v = √GM/r
4- The time taken for a satellite to make one orbit is called the orbital period, T
5- Speed = distance/time and the distance for a circular orbit is 2πr so v = 2πr/T
6 - Rearrange for T to get T = 2πr/v
7- Sub the expression for v we found earlier into T = 2πr/v
8 - Rearrange to get T^2 in terms of r^3 where the constant of proportionality is 4π^2/GM
Explain how a satellite will move around a planet/star at a constant speed but will be constantly accelerating
- A satellite will move around a planet/star at a constant speed but will be constantly accelerating because the centripetal force on the satellite is at right angles to the velocity
- Therefore, there is no component of the force in the direction of the velocity to increase or decrease the size of it
- The force does no work on the satellite and so there is no change in the kinetic energy of the satellite
- The satellite is always accelerating towards the centre of mass of the star/planet which it is orbiting
Show how the relationship T^2∝r^3 can be applied to questions
Ta^2/ra^3=Tb^2/rb^3 where a and b are two different orbiting objects
Describe the conservation of energy for an orbiting object which moves to another orbit from the one it started with
If a satellite is in a circular orbit and moves to another circular orbit then the sum of potential and kinetic energy will not be the same
Explain the conservation of energy for an orbiting satellite in both a circular orbit and an elliptical orbit
- An orbiting satellite has kinetic and potential energy, its total energy (KE + GPE) is always constant
- In a circular orbit a satellite’s speed and distance above the mass its orbiting are constant. This means that its kinetic energy and potential energy are also both constant
- In an elliptical orbit a satellite will speed up as its height decreases and slow down down as its height increases. This means that its kinetic energy increases as its potential energy decreases and vice versa so the total energy remains constant
How often do Geostationary satellites orbit the Earth?
Geostationary satellites orbit the Earth once in 24 hours. Their orbits take exactly one day
What is a synchronous orbit?
A synchronous orbit is one where the orbital period of the orbiting object is the same as the rotational period of the orbited object
What is the relationship between Geostationary satellites and synchronous orbits?
Geostationary satellites are a type of synchronous orbit, they are always above the same point on Earth. To do this they must always be directly above the equator - their plane of orbit follows the Earth’s equator
What angular speed do Geostationary satellites travel with?
A Geostationary satellite travels at the same angular speed as the Earth turns below it
What is the orbital radius of Geostationary satellites?
Their orbital radius is about 42000km and about 36000km above the surface of the Earth
What are Geostationary satellites mainly used for?
Geostationary satellites are useful for sending TV and telephone signals, the satellite is stationary relative to a certain point on the Earth so you don’t have to alter the angle of your receiver or transmitter to keep up
What are low orbit satellites?
Low orbiting satellites are defined as any satellites which orbit between 180-2000km above the Earth
Why are low orbit satellites useful for communications?
- Satellites designed for low earth orbits are cheaper to launch and require less powerful transmitters as they are closer to Earth
- This makes them useful for communications. However, their proximity to Earth and relatively high orbital speed means you need multiple satellites working together to maintain constant coverage
How do low orbit satellites see the Earth’s surface?
Low orbit satellites are close enough to see the Earth’s surface in a high level of detail. Imaging satellites are usually placed in this type of orbit and are used for things like spying and monitoring the weather
Where do the orbits of low orbiting satellites usually lie?
Their orbits usually lie in a plane that includes the north and south pole
How can low orbiting satellites scan the whole surface of the Earth?
Low orbiting satellites rotate at much higher angular speeds than the planets they orbit and so they scan the whole surface of the Earth
What is the relationship between a charged object and electric fields?
Any object with charge has an electric field around it
What is the electric field of a charged object?
The electric field of a charged object is the region where it can attract or repel other charges
What is electric charge (Q) measured in?
Electric charge (Q) is measured in coulombs (C) and can be either positive or negative
Explain which charges attract each other and which repel each other
- Oppositely charged particles attract each other
- Like charges repel each other
What happens when a charged object is placed in an electric field?
If a charged object is placed in an electric field, it will experience a force
Where is the charge concentrated if a charged object is a sphere?
If a charged object is a sphere you can assume all of its charge is at its centre
What are electric fields?
Electric fields are force fields where charged objects will experience a non-contact force
What is the relationship between electric fields and field lines?
Electric fields can be represented by field lines
What is the purpose of Coulombs law?
Coulomb’s law gives the force of attraction or repulsion between two point charges in a vacuum
State Coulombs law
The force acting between two charged bodies is inversely proportional to the square of the distance between them and directly proportional to the product of the magnitude of the two charges
State the equation given by Coulombs law and each of its variables
- F = Q1Q2/4πε0r^2
- ε0 is the permittivity of free space measured in Fm^-1
- Q1 and Q2 are the charges
- r is the distance between Q1 and Q2
Show the rules of proportion for the Coulombs law equation
- F = k*Q1Q2/r^2
- k = 1/4πε0
- F = Q1Q2/4πε0r^2
What is the relationship between the force on Q1 and Q2?
The force on Q1 is always equal and opposite to the force on Q2 - the direction depends on the charges
Is the force between two point charges positive or negative if the charges are opposite?
If the charges are opposite then the force is attractive so the force (F) will be negative
Is the force between two point charges positive or negative if the charges are alike?
If the charges are alike then the force is repulsive so the force (F) will be positive
What type of law is Coulomb’s law?
- Coulomb’s law is an inverse square law
- The further apart the charges, the weaker the force between them
If the point charges aren’t in a vacuum, what does the size of the force between them depend on?
- If the point charges aren’t in a vacuum, then the size of the force F between them also depends on the permittivity of the material between them
- Air can be treated as a vacuum when using Coulomb’s law
Define electric field strength
- Electric field strength (E) is the force per unit positive charge
- It’s the force that a charge of +1C would experience if it was placed in the electric field
State the formula for calculating electric field strength and its variables
- E = F/Q
- F is the force on a test charge
- E is the electric field strength measured in NC^-1
- F is the force and Q is the charge
Is electric field strength (E) a scalar or a vector?
E is a vector pointing in the direction that a positive charge would move
What are the units of electric field strength?
Newtons per Coulomb (NC^-1)
What does electric field strength depend on?
Where you are in the field
What type of field does a point charge have?
A point charge or any body that behaves as if all its charge is concentrated at the centre has a radial field
On an electric field line diagram what does it mean if the field lines point away from the object?
The object in the field has the same positive/negative charge as the object whose field its in so it would be repelled away from the object
On an electric field line diagram what does it mean if the field lines point towards the object?
The object in the field has the opposite positive/negative charge as the object whose field its in so it would be attracted towards the object
What is the relationship between electric field strength and distance from the point charge in a radial field?
In a radial field, E is inversely proportional to r^2
State the formula used to calculate electric field strength in a radial field
- E = Q/4πε0r^2
- Q is the point charge
How does electric field strength change as you go further away from the point charge?
Field strength decreases as you go further away from Q - on a diagram the field lines get further apart
State the inverse square law relationship between electric field strength and distance and draw a graph to show this relationship
- E ∝ 1/r^2
See page 127 in the revision guide
In a uniform field, what is the relationship between E and d?
In a uniform field, E is inversely proportional to d
How can a uniform field be produced?
- A uniform field can be produced by connecting two parallel plates to the opposite poles of a battery
- The field strength is the same at all points between the two plates
State the formula used to calculate the electric field strength between two plates
- E =V/d
- V is the potential difference between the plates in V
- d is the distance between the plates in m
How can uniform electric fields be used to determine whether a particle is charged or not?
The path of a charged particle moving through an electric field will bend, the direction it bends depends on whether its a positive or negative charge
Explain how to determine whether a particle is charged or not as it passes through a uniform electric field
1- A charged particle that enters an electric field at right angles to the field feels a constant force parallel to the electric field lines
2- If the particle is positively charged then the force acts on it in the same direction as the field lines. If it’s negatively charged, the force is in the opposite direction to the field lines
3- This causes the particle to accelerate at right angles to the particle’s original motion and so it follow a curved path (a parabola)
Define absolute electric potential
The absolute electric potential at a point is defined as the work done in taking unit positive charge from infinity to that point.
All points in an electric field have an …
absolute electric potential (V)
What does the absolute electric potential of a point depend on?
The absolute electric potential of a point depends on how far it is from the charge creating the electric field and the size of that charge
State the formula for calculating absolute electric potential in a radial field
- V = Q/4πε0r
- V is the absolute electric potential
- Q is the size of the charge
- r is the distance from the charge
Is electric potential a scalar or vector quantity and what are its units?
- It is a scalar quantity
- Measured in volts or J/C
If an object enters an electric field how can we calculate its speed, acceleration, etc..?
- We treat it as a projectile so we consider its horizontal and vertical components of velocity separately and to find its overall velocity we find the resultant of these two velocities
- To find acceleration use F=EQ=ma
What does the sign of electric potential (V) depend on?
It depends on the charge Q:
- V is positive when Q is positive and the force is repulsive
- V is negative when Q is negative and the force is attractive
When is the absolute magnitude of electric potential (V) the greatest?
- The absolute magnitude of V is the greatest on the surface of the charge and decreases as the distance from the charge increases
- V will be zero at an infinite distance from the charge
Draw a graph of V against r for a repulsive force and explain it
- V is initially positive and tends to zero as r increases towards infinity
- See page 128 in the revision guide
Draw a graph of V against r for an attractive force and explain it
- V is initially negative and tends to zero as r increases towards infinity
- See page 128 in the revision guide
What does the gradient of a tangent to a graph of V against r for either an attractive or repulsive force give?
The gradient of a tangent to either graph gives the field strength at that point
How can you calculate the change in electric potential from a graph of E against r?
The area under the graph between two points in question
Define electric potential difference
Electric potential difference is the energy needed to move a unit charge
If two points in an electric field have different potential, what do they have between them?
If two points in an electric field have different potential then there is an electric potential difference between them
To move a charge across a potential difference what do you need?
To move a charge across a potential difference you need to use energy
What does the amount of energy needed to move a charge across a potential difference depend on?
The amount of energy you need to move a charge across a potential difference depends on the size of the charge you’re moving and the size of the potential difference you want to move it across
State the two formulas you can use to calculate the energy needed or work done to move a charge across a potential difference
- Fd = QΔV
- ΔW = QΔV
- F is the force on the charge (N)
- d is the distance that the charge moves (m)
- Q is the charge being moved (C)
- ΔV is the electric potential difference and ΔW is the work done
Derive the work done formula (ΔW = QΔV)
- There are two parallel plates with a potential difference of ΔV across them creating a uniform electric field
1- The field strength is given by E = F/Q = ΔV/d
2- This rearranges to give the formula Fd = QΔV
3- To move a charge Q from A to B the work done = force * distance moved = Fd so ΔW = Fd
4- So the work done in moving a charge Q through a potential difference of ΔV is given by ΔW = QΔV
Derive the work done formula for moving an object in a gravitational field (ΔW = mΔV)
- At the Earth’s surface the gravitational field is uniform
- The field strength is g = - ΔV/Δr = F/m
- This rearranges to give mΔV = -FΔr
- To throw a ball m from A to B the work done = force* distance moved = mΔV
- So the energy needed to move a mass m against a gravitational potential difference is given by mΔV
What is the relationship between electric fields and equipotentials?
Equipotentials are found in electric fields as well as gravitational fields
What are equipotentials for a point charge and parallel plates?
- For a point charge the equipotentials are spherical surfaces
- Between parallel plates the equipotentials are flat planes
Describe how an electric charge would travel along an equipotential
As no work is done when travelling along an equipotential, an electric charge can travel along an equipotential without any energy being transferred
What is the general difference between the gravitational and electric field equations?
They are usually the same formulas with Q instead of M or m and 1/4πε0 instead of G
Draw a table of the formulas for gravitational and electric fields for Force due to, Field strength and potential
See page 130 in the revision guide
What is the main difference between gravitational forces and electric forces?
Gravitational forces are always attractive whereas electric forces can be attractive or repulsive
When calculating the gravitational and electrostatic forces between subatomic particles what formulas do we use and why?
- We use the regular newtons and coulomb’s law formulas
- Gravity can be ignored as although the particles are close together they have small masses so the gravitational force at these distances is much weaker than the electrostatic forces
- The nucleus doesn’t break apart from the electrostatic repulsion due to other forces acting
