Unit 4.2 - Electrostatic and gravitational fields Flashcards
What’s similar about electrostatic and gravitational fields?
Both have very similar forms
What does the gravitational field of the earth provide?
A constant acceleration of 9.81ms^-2
When is using the constant acceleration of 9.81ms^-2 from the gravitational field of the earth a useful method?
When we consider small changes in height above the surface of the earth
What is a field in physics?
A model of a physical quantity, typically a number, that has a value for each point in space and time
Scalar fields
Will have a value only at different points
Example of a scalar field
The temperature at different positions around the country
Vector fields
Have a value and a direction related to their position
Describe and give an example of a vector field
On a weather map, the surface wind velocity is described by assigning a vector to each point on a map. Each vector represents the speed and direction of the movement of air at that point.
What is a gravitational field?
A model used to explain the influence that a massive body extends into the space around itself, producing a force on another massive body (a body that has mass)
= force per unit mass
What is used to explain gravitational phenomena?
A gravitational field
What is a gravitational field measured in?
Newtons’s per kilogram
How has the way gravity has been explained changed over time?
Original concept —> gravity was a force between point masses
Then —> gravity was some kind of radiation field or fluid
Now —> gravity is taught in terms of a field model rather than a point attraction
Describe what a field model is and what happens in it
Rather than two particles attracting each other, the particles distort space-time via their mass, and this distortion is what is perceived and measured as a “force”
What is measured as a force in a field model?
Particles distorting space-time via their mass
What does mass do to space-time?
Curves it
Describe space- time when there’s no mass
Flat
Describe space-time where there is a mass
Curvature towards the mass
What will happen to two masses in a field model and why?
Will attract each other due to the curvature caused by the mass
Where will masses fall in the field model with a large and small mass?
The smaller mass will fall towards the large mass
How does matter move in the field model?
In certain ways in response to the curvature of space-time
Describe the gravitational force in the field model
There is either no gravitational force or gravity is a fictuous force
Way of imagining the field model
Consider a heavy mass on a flexible surface
What is the only thing that’s significant to the object causing the curvature of space-time in field model?
The mass of the object
What is not significant to the curvature of space-time caused by an object in the field model?
The size of the object
What can we consider the mass of a body to be in the field model?
The point at the centre of the body - the centre of the mass
Where do we consider the weight of objects to act?
At the centre of gravity
Why is the field theory used to explain the origin of the solar system?
All planets orbit in the same direction (in the example of the heavy mass on a flexible surface, it’s the friction that causes the objects to eventually fall)
Field lines
“Imaginary” force lines which describe the effect of a field at that point
What can we consider field lines to be?
The gradient of the field
Example of field lines in real life
On maps, contour lines join areas of equal height above sea level
What does the gradient of field lines relate to?
The proximity (nearness) of the contour lines
What do closer field lines indicate?
A higher area (steepest slope)
What do further away field lines indicate?
Lower areas (less steep slope)
As field lines reperesent height, what do they also represent?
Potential
What does a higher field line mean?
A higher potential
When we consider a point mass, describe the space-time surrounding it
Is curved in a radial manner surrounding it
What is a point mass in the field model the opposite of and why?
The opposite of a “hill” on a map since other masses “fall” towards it
Where is a point mass on a field model and why?
At the bottom of the “well” since it’s causing the curvature
What are the lines going into the well on a field model?
Field lines
Would do field lines represent?
The direction that an object would move
What do the circular lines on a field model represent?
Equipotentials
What do equipotentials on a field model show?
That an object has the same potential anywhere along the line
In which direction would a mass placed anywhere in a field experience a force?
Towards the potential well
What is the height from a point mass on an equipotential diagram associated with?
A potential energy
What happens to the height as you go further out from the centre on an equipotential diagram and why?
Is increasing because the point mass is at the lowest point in the field
If there’s a small gradient in the field model, describe the force
Small
If there’s a big gradient in the field model, describe the force
Big
Which lines represent the direction a mass would experience a force?
Field lines
What do field lines represent?
The direction a mass placed here would experience a force
What can the value of the force on an object in a field be calculated by?
The potential gradient
What is field strength measured in?
Force per kg
What is field strength the same as?
The potential gradient
Where is the highest gradient in an equipotential diagram?
In the middle of
Describe the change in force when going out from the centre of an equipotential diagram
There isn’t a linear change in force - it follows the inverse square law
Explain with an example the inverse square law in an equipotential diagram
Double the distance, the field is 4x weaker
What type of forces can we have in an electrical field?
Attractive and repulsive forces
What are the only type of forces we can have in a gravitational field?
Attractive,
In what type of field can we only have gravitational forces and in what type can we have repulsive forces too?
Gravitational
Electrical
What type of region is a gravitational field?
A region where a mass exerts a force on another mass
Why are the equipotential lines always formed into a well in gravitational fields?
Since gravity is always attractive
Why is electric force defined as having an effect on?
A positive charge
What does it mean since electric force is defined as having an effect on a positive charge?
There are two possible illustrations for the field surrounding point charges, dependent on their polarity
What are the two fields in electrical fields
The field due to a positive charge and the field due to a negative charge
What will a positive charge do at the field due to a positive charge
Will fall down the gradient into the potential well
What does a negative charge do in the field due to a negative charge
Goes up the gradient out of the potential well (anti-gravity)
What is the size of a gravitational force calculated according to?
Newton’s law of universal gravitation
Newton’s law of universal gravitation
Every massive particle in the universe attracts every other massive particle with a force that is directly proportional to the products of their masses and inversely proportional to the square of the distance between them
How do we measure the distance between objects when calculating the gravitational force?
We take the distance between them from the centre of mass
What should the particles be when using the universal law of gravitation and when does this not matter?
Spherical
If there’s a great enough distance between them, it doesn’t matter much
Equation to describe Newton’s law of universal gravitation
F = GM1M2/r^2
Equation to calculate the force between two masses
F = GM1M2/r^2
G
Universal gravitational constant
r^2 in the equation for the force between two masses
The distance between the two masses
How do we know that the equation for the force between two masses is an inverse square law?
It includes r^2
Why is the force between two masses almost nothing and when does this change?
Since the vale of G s tiny
The force is bigger when masses are present
Gravitational field strength
The force per unit mass on a small test mass placed at a point
Gravitational field strength equation
g = GM/r^2
Why is the gravitational field strength equation how it is?
We consider M2 to be 1kg
What is the distance between two objects that are touching if we need to calculate the force between them and why?
Equal to the sum of their radii
It’s the distance between the centres of gravity of the objects
What does the electrical field only apply to?
Charged object
Do the equations have a similar form for both electrical and gravitational fields? What is different?
Yes, it’s just hat electrical fields only apply to charged objects
Coulomb’s law
The force between two point charges is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance between them
How is Coulomb’s law different to Newton’s law of universal gravitation?
They’ve both got the same wording, it’s just that “masses” and “charges” are used
Equation for the force between two charges
F = 1/4piε0 Q1Q2/r^2
What will happen if both of the charges are the same when calculating the force between two charges?
They will repel
Electrical field strength equation
E = 1/4piε0 Q/r^2
Why is the electrical field strength equation how it is?
Q2 is assigned the value of +1C
What is the electrical field strength equation true for?
A field in a vacuum or air
What would happen if an electrical field strength were in another substance that isn’t air to the electrical field strength equation?
εr would change the value, but we won’t encounter this
What can 1/4piε0 be taken as as an approximation?
9x19^9 (which is in the data book)
Potential
The energy per unit charge/mass at that point in the field
Where in a field is there no effect?
At the level of zero potential
Describe zero potential
Flat space
Describe the work when the field does the work
Negative work
Describe the work when you have to put work into the field
Positive work
What work will be required to take an object from infinity to another point?
Negative
What does it mean if the work is negative?
The field does the work
How is the potential defined at infinity?
Zero
When would the work don in a field be even higher?
If moving to a point nearer the centre of the mass
If a mass has moved even closer to the centre of the mass, describe the work
Larger negative number
What type of value is the potential anywhere due to any mass going to be?
Negative
Why is the potential anywhere due to any mass going to be negative?
Since the potential decreases as we approach the mass and it starts at zero at infinity
Does potential have a direction? Why?
No, since potential is a scalar field (like the temperature map)
What is field strength equal to?
Potential gradient
Describe the force an object experiences at a higher potential gradient
Bigger
At what potential gradient does an object experience a bigger force?
Higher potential gradient
How do we define potential in electrical fields compared to gravitational fields?
Gravitational fields = unit mass
Electrical fields = unit positive charge
What does the work needed to bring a unit positive charge to a point in an electrical field depend on?
Whether it is a positive or negative charge causing the field
What will a positive charge require to move the positive charge closer to it?
Positive external work
What will a negative charge require to move a positive charge towards it and what does this mean?
Negative external work
The field does the work
What do we need to consider to calculate the value of the potential in both electrical and gravitational fields?
The field strength
Field strength
Force per unit charge/mass
Describe the forces in a gravitational field
Small (but big masses)
describe the forces in an electrical field
Big (but small charges)
Comparing the different lines in a field to the map analogy, what can the different lines be compared to?
Equipotentials (lines of equal potential) are equivalent to the contour lines
Force lines are equivalent to the gradient on the map
What is force in a field?
The potential gradient
Potential gradient equation
Potential gradient = Change in potential/distance = force
Expression for the potential at a point in a gravitational field
Vg = -GM/r
Difference between forces and potentials equations
Potentials —> r
Forces —> r^2
Why is the negative sign in the expression for potential at a point in a gravitational field?
Since all potentials are negative
Equation for the potential in an electrical field
VE = 1/4piε0 Q/r
What will the polarity of the potential in an electrical field come from?
The polarity of the charge present
Explain how the polarity of the potential in an electric field will come from the polarity of the charge present
If it is a negative charge, the potential will be negative
If it is a positive charge, the potential will be positive
What is done to calculate the potential energy of an object of a given mass/charge?
The potential is multiplied by the value of the field potential at the point where the object lies
Equation for the potential energy of an object of a given mass/charge
Vg = -GM1M2/r
Equation for the potential energy between two charges
VE = 1/4piε0 Q1Q2/r
Where will there be no work done in n electrical field?
At the very top of the dip before entering it
Describe the work done when moving towards the mass
Work is always done by the field
Vg
Gravitational potential
VE
Electrical potential
Which sign is always negative - Vg or VE?
Vg
What does the sign of VE depend on?
The size of the charge causing the field
How, basically, do we work out potential energy?
Potential x mass/charge
What can we use potential energy to work out?
The maximum kinetic energy
At what angle do fields come from point charges every time?
90 degrees
What come from point charges at 90 degrees every time?
Point charges
Where does an electric field go from and to?
From the positive charge to the negative charge
Where is in the highest force in an electric field pattern?
In the negative well
4 electric field patterns to learn
Point positive charge
Point positive and point negative charge
Row of negative charges and point positive charge
Row of positive and negative charges (capacitor)
Why is calculating the net potential due to several masses or several charges very straightforward?
They are simply overlapping scalar fields
What is the analogy to explain calculating the net potential due to several masses or several charges/
Imagine placing a temperature map of a winer’s day over a similar map in the smear, as if both days happen simultaneously. The net effect will give the total temperature of both days.
What is the net effect of the overlap of two potential maps?
The addition of the potential due to each field
Explain an example where the potential would decrease in a specific point when working out the net potential due to more than one mass/charge
If one field is negative and the other positive (only possible for charges), then the potential is reduced at that point.
What is the only situation in which it’s possible for one field to be negative and one to be positive when calculating the net potential?
Only possible for charges
When does the net potential become zero?
When both of the fields are equal and opposite
How do we calculate the potential at a point?
Just calculate the potential due to each mass or charge present and add them up
What are all of the potential values with gravitational potential?
Negative
What do the + and - charges depend on when working out net potential with charges?
Depend on the charges
What type of field is the force field and what does this lead to?
Vector field
Direction has to be considered when adding the net effect of fields due to more than one mass/charge
When does direction have to be considered when working out its net amount and why?
For net field strengths or net forces
They’re vector fields
How is wind pattern observed in reality?
It’s a resultant of all the individual pressure gradients due to the difference in the density of the air over the country
What would we get if both weather systems “overlap” and what is this used as an analogy of?
A “resultant wind”
Net field strength or net force due to more than one mass/charge
How is wind pattern observed?
Is a resultant of all the individual pressure gradients due to the difference in the density of the air over the country
Why is the direction of the field due to each mass always obvious with the gravitational force?
It’s always attractive
How is the size of field strength calculated?
Using g = GM/r^2
M = mass of the body
r = distance from the point to the centre of the body
Calculation for working out the net field force, for example between the earth and the moon
g(earth)-g(moon) and then if the value is negative then g(moon)>g(earth) and the field direction would be towards the moon
When is the vector addition with net field strength or net force straightforward?
When the masses are in a line
What do we do in order to work out the net field strength or net force when the point lies off the line joining the two masses?
Then the horizontal and vertical components of the field are added as vector - just like with forces in unit 1
What types of forces are there for charges?
Both attractive and repulsive
What will most exam questions be on in terms of net field strength or net force calculations?
Charges
What is the field direction with charges?
The direction in which a positive charge would move
When is there an attractive force with charges?
When negative
When is there a repulsive force with charges?
When positive
How is the magnitude of the force between charges calculated?
Using E = 1/4piepsilon0 Q/r^2
In some situations, how is it easier to get the direction of the field when working out the net field strength or net force due to more than one mass/charge?
It may be easier not to include the polarity of the charge and simply use arrows to get the direction of the field
How can we plot equipotentials due to different combinations and shapes of charges?
A point charge can be produced using the tip of a wire
A line of charge can be produced using a strip of conductor
How can we produce a point charge?
Using the tip of a wire
How can we produce a line of charge?
Using a strip of conductor
How are field lines plotted compared to the equipotential lines?
At 90 degrees
What are field lines at 90 degrees to?
The equipotential lines
What is field strength equal to?
Force and potential gradient
If we plot a graph of potential at various points in a field, what will the gradient show?
The field strength
Unit of field strength
Arbitrary units
What does a steeper slope when plotting a graph of potential at various points in a field mean?
A stronger field
Where are the peaks on 3D graphs of field strength?
At point positive charges
Where are the troughs on 3D graphs of field strength?
At point negative charges
What will a graph of field strengths with a row of positive charges and a row of negative charges show and what does this represent?
The graph will be a steady slope from high to low voltage
Represents a capacitor
How is the direction of the field visualised when creating graphs of field strengths?
Since the direction of movement of a positive charge placed here is clear to see
What would we do in the case of the following question?
“Calculate the work done when a +1.0nC charge is brought from a large distance way and placed at P”
Since it’s coming from a “large distance away”, the change in potential will be from zero to that point
So since W = qdeltaV, we just need to work out V at P
Vp = 1/4piepsilon0 x Q/r
Then multiply V by the charge (1nC)
When do we know that we can calculate a change in potential as from zero to that point?
If the object is coming from a large distance away
What are the two ways in which we could calculate the work needed to raise a mass of 1kg through a distance of 2m near to the earth?
- Using work done = energy transferred and Ep =mgh
- Using work done =energy transferred and Ep = Vgm
Both will give the same answer
Is Ep = mgh valid?
For most everyday calculations, yes
Worded and equation definition of an electrical field
The electric Coulomb force per unit charge
E = f/q
Worded and equation definition for a gravitational field
The gravitational force per unit mass
g = f/m
What do we do if there are ever any questions in this unit involving protons?
Remember that they have the same charge as an electron, just positive
Charge of a proton
Same as an electron just positive
What does the sum of kinetic and potential energy always make up and what does this mean?
Always remain constant at each point of motion, and so any change in PE will be equal to the KE which we can use to work out other factors
Electrical field unit
NC-1
Gravitational field unit
Nkg-1
Electric potential unit
JC-1
Gravitational potential unit
Jkg-1
What will the resultant electric field strength be a long distance away from two charges and why?
Zero
The fields from the charges will cancel
What happens to the resultant force from charges with increasing distance and why?
Decreases
Inverse square law
Why does the resultant force from charges decrease with distance
Due to the inverse square law
Gravitational potential at a point
Work done per unit mass from infinity
Electric potential
The work done per unit charge in bringing a charge from infinity to that point
Direction of magnetic fields
Positive to negative
Equation for working out the force in an electric field + explain
F = EQ
It comes from the F = 1/4pi x Q1Q2/r^2 equation, where Q2 becomes the other Q
E is E = V/d
What’s similar about gravitational and electric fields?
Vectors
Obey inverse square law
Both are attractive fields (electric can be repulsive too)
Electric field strength E
The force per unit charge on a point positive charge (vector)
Electric potential V
The work done per unit charge in bringing the charge from infinity to that point
What do we always need to say when describing potentials?
Work done
Similarities and differences between electric and gravitational fields
Similarities:
-same shape field
-obey the inverse square law
-vectors
-both lead to PE
-PE proportional to 1/distance
-fundamental force laws
-vectors
Differences:
-E.fields = force per unit charge
G.fields = force per unit mass
-E. fields = attractive and repulsive
G. fields = only attractive
-Gravity is far weaker on a small scale, but electrical negligible on a large scale
-E potential = work done per unit charge
G potential = work done per unit mass
-E fields depend on permittivity
-G fields depend on dark matter
Explain why all gravitational potentials are negative
Since the potential at infinity is zero and work is done in an object to get to infinity
