Electric Fields Flashcards
What is an electeic field
A region in which a charged body will experience a force
Like charges
Repel
Charges … electric fields and charges … with electric fields
Create
Interact
Opposite charges
Attract
Electric field lines
Show the direction of force that would be experienced by a small positive test charge if it were placed at that point on the field
Graphical representation of direction and relative strength of a field with arrows indicating direction
Closer means stronger force
Equipotentials
Perpendicular to field lines
Join points with equal potential
No work done on a test charge if it moves along an equipotential
Coulomb’s law of attraction
The force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of their separation
Express Coulomb’s law of attraction mathematically
F=1/4piĘ0 x Q1Q2/r^2
What does the coulomb charge depend on
The signs of the two charges
What is the permittivity of free space
A measure of how easily an electric field passes through a vacuum
Farad per meter as the unit
Electric field strength units
V/m
N/C
Absolute potential energy
Work done in moving a charged object from infinity to that point in an electric field
If the force is attractive then what happens to the potential energy
Decreases
More negative
Get closer
If a force is repulsive what happens to the potential energy
Increases
Less negative
Move away
Electric potential energy for two objects at infinite separation
Zero
Equation for electric potential energy
Ep=1/4piĘ0 x Q1Q2/r
Equation for electric potential energy
Dd
How do you handle signs for potential energy
Keep in equation
What happens when a positive charge is brought towards another positive charge
Charges repel
Work has to be done to overcome repulsion
Potential energy increases
So two positive charges have a positive potential energy
What happens if two negative charges are brought towards eachother
Charges repel
Work must be done to overcome this repulsion
So potential energy increases
So two negative charges have positive potential energy
What happens a positive charge is brought towards a negative charge or vice verse
Charges attract
So no work has to be done to bring them together
Instead kinetic energy of charges will increase as they move closer
And potential energy decreases from zero to be more negative
So two unlike charges have negative potential energy
Absolute electric potential
The work done per unit charge on moving a small positive test charge from infinity to that point in the field
Units fir electric potential
J/C
Electric potential equation
V=1/4piĘ0 x Q/r
Where Q is the charge of the thing creating the field
Positive value for change in potential
Work has been done on the charge to move it from its initial to its final position
What does a negative value of potential mean
The field does work on the charge and it moves on its own
Force and separation ratio
F1r1^2=F2R2^2
Field strength and separation ratio
E1r1^2=E2r2^2
Potential and separation ratio
V1r1=V2r2
Potential energy and separation
Ep1r1=Ep2r2
Area under a force separation graph
Work done moving between two points
W=Fs
Area under a field strength separation graph
Change in potential between two points
E=-V/r
Gradient of a potential separation graph
Magnitude of field strength at that point
E=-V/r
Gradient of a electric potential energy separation graph
Force acting at that point
F=W/s
Explain the force and field strength inside a hollow conducting sphere and the potential and potential energy
Force is zero
Field strength is zero
Potential is constant
Potential energy is constant
9Since no further work is done in bringing the charge from infinity once you get past the surface of the sphere)
Similarities between electric and gravitational fields
Force and field strength are inversely proportional to the separation squared
Potential and potential energy are inversely proportional to separation
Differences between electric and gravitational fields
Gravitational fields are always attractive but electric can be attractive or repulsive
Gravitational potential/potential energy is always negative but electric potential/potential energy can be positive or negative
G is the constant for gravitational fields whereas e0 is the constant for electric fields
Electric fields usually more important on a small scale in atoms and nuclei but gravitational is usually more important on a larger scale with respect to planets and galaxies
How did Millikan conduct an experiment to measure the charge of an electron
Adjusted the potential difference across two parallel plates
To make a charged oil drop hover in the uniform electric field between the plates
How does field strength vary between two parallel plates
Doesn’t
Same everywhere
Uniform
Equation to calculate the force on an electron passing through two parallel plates
F=Eq
E=V/d
How do you calculate the speed of an electron as it enters two parallel plates
E=1/2mv^2
E=QVolts
Why are capacitors good
Don’t have resistance associated with them
So good for storing and quickly releasing energy
What is a capacitor
A device that stores and releases charge
Pair of metal plates separated by a thin layer of an insulator (dielectric)
So charge can be stored on the plates but can’t flow across the gap
Capacitance
The charge stored per unit potential difference across the plates of the capacitor
Must include the numbers if given
Equation for capacitance
C=Q/V
Capacitance is measured in Farads, C/V
Gradient of a charge potential difference graph
Capacitance
Area of a charge potential difference graph
Energy stored in capacitor
When will a capacitator stop charging
When its potential difference is the same as the power supply
Equations for energy stored in a capacitor
E=1/2QV
E=1/2CV^2
E=Q^2/2C
Capacitance given the area and separation
C=Ae0er/d
What is a dielectric
Material placed between two parallel plates in a capacitor
Which increases the capacitance
What makes a good capacitor
Large surface area
Small separation
Large relative permeability of dielectric
Does the capacitance change in Q=CV
No
Structure of a dielectric
Consists of polar molecules
That line up in the electric field between the plates
Explain the effect of a dielectric on a fixed charge capacitor in isolation
The presence of molecules negative charges near to the positive plates makes it positive potential less
The presence of molecules positive charges near the negative plates makes its negative potential less negative
So the potential difference across the plates has now decreased
Since Q is fixed because it still stores the same charge and C=Q/V, decreased potential difference means an increased capacitance
Energy stored, given by 1/2Q^2/C is now less
Some energy has been used to align the polar molecules
Explain the effect of a dielectric on a fixed potential difference cell
The presence of molecules negative charges near to the positive plates makes it positive potential less
The presence of molecules positive charges near the negative plates makes its negative potential less negative
The potential difference between the cell and the capacitor plates now drives a current
Current increases the charge on the capacitor plates which in turn increases the potential difference
The potential difference across the fully charged capacitor is the same as before but the charge stored has increased
The insertion of a dielectric between the capacitor plates increases the energy stored
Better to insert the dielectric before charging
Equations for discharging a capacitor
Q=Q0e^-t/RC
I=I0e^-t/RC
V=V0e^-t/RC
Explain RC in charging and discharging
The time constant
The time in seconds it takes for the charge to fall or rise to 1/e of its original value (37%)
Higher the RC…
Longer capacitor takes to discharge or charge
What is the theoretical discharge time
5RC
The theoretical time to discharge a capacitor
After 5RC only 0.69% of original remains
5RC
Time to fully discharge or charge a capacitor
Gradient of a discharging charge time graph
Discharge current
Area of a discharging current time graph
The charge lost
How much charge of original remains after 3RC
5.07%
Explain the exponential discharge curve
The potential difference across the capacitor drives a current through the resistor
Current is the rate of flow of charge, so the charge on the capacitor plates decreases as energy is transferred
As the capacitors charge decreases so does the potential difference
So the current driven by the potential difference decreases
So the rate of change of charge on the plates decreases
Rate of change of potential difference also decreases as the capacitor discharges
How does charging a capacitor work
When a capacitor is in a circuit with a cell, resistor and closed switch, current is driven by the potential difference
The current transports electrons from one capacitor plate to the other
This increases the potential difference across the capacitor until it is equal to the p.d
Which is when the current has dropped to zero and the p.d across the resistor is zero
Charging capacitor equations
Q=Q0(1-e^-t/RC)
V=V0(1-e^-t/RC)
I=I0e^-t/RC
Gradient for a charging charge time graph
Current
Area for a charging current time
Charge gained
Theoretical charge time
5RC
The theoretical time to charge a capacitor
After 5RC 99.31% of maximum charge
Explain the exponential charging curve
The potential difference across the resistor drives a current through the resistor
The current is the rate of flow of charge so the charge on the plates increases as electrons are transferred from the positive plate to the negative plate
As the charge on the capacitor plates increases so does the potential difference
As the potential difference across the capacitor plates increases, Kirchhoff’s Second Law requires the potential difference across the resistor to decreases
So current through the resistor decreases which means the rate of increase in the charge on the capacitor plates decreases
So the rate if change of potential difference, charge and current all decrease as the capacitor charges
Give a method to explain how you can demonstrate constant rate discharge
Close switch to charge capacitor
Until voltmeter reading = supply p.d
Open switch and close other switch to discharge capacitor
Decrease resistance of variable resistor to maintain a constant current
Record p.d every 20 seconds until ~0V and capacitor is discharged
Plot a graph
How do you show a graph is exponential
Read initial value on y axis Half Find time taken for this decrease by 50% Repeat for 50% to 25% etc Use mean time as best estimate If the graph is exponential then the time to reduce by half should be constant
How do you graphically show that a curve of discharging is exponential
Plot a graph of Ln Q V or I against time
If the graph is exponential then it should be linear
How can you chose a suitable resistor to perform the capacitance experiment
Effect of resistance influences time constant
Increasing resistance increases time constant so increases discharging time
Too small and you won’t have enough time to get enough readings since decrease too fast
Too big and the readings will hardly change and produce a very large graph
