3.7 Fields and their consequences Flashcards
What is a force field?
A region in which a body experiences a non-contact force
What is newton’s law of gravitation?
Magnitude of gravitational force between two masses is directly proportional to the product of the masses, and is inversely proportional to the square of the distance between them
What is meant by gravitational field strength?
Force per unit mass exerted by a gravitational field on an object
Gravitational field strength equation: general
g = F/m
Gravitational field strength equation: radial field
g = GM/r²
What is meant by gravitational potential?
The work done required in bringing a unit mass from infinity to the point
What is meant by gravitational potential difference?
The energy required to move a unit mass between two points
Why is gravitational potential energy negative?
- Gravitational potential energy is zero at infinity
- As an object moves from infinity to a point, energy is released as the gravitational potential energy is reduced
- Therefore gravitational potential energy is always negative
How to derive T² = k r^3
Centripetal force = Gravitational force
What is meant by escape velocity?
Minimum velocity an object must travel at in order to escape the gravitational field of a mass
How to derive escape velocity = sqrt(2GM/r)?
kinetic energy = gravitational potential energy
What is a synchronous orbit?
When the orbital period of the satellite is equal to the rotational period of the object that it is orbiting
What is a geostationary orbit? What are its features?
- A synchronous orbit (24 hours) and they always stay above the same point on the Earth, because they orbit directly above the equator
- Only one particular orbit height is possible
- Travels west to east
Application of low-orbit satellites?
Monitoring weather and military applications
What is meant by electric field strength?
Force per unit positive charge experienced by an object in an electric field
E (electric field strength in general) equation
E = F/Q (by definition!)
E (electric field strength for uniform fields formed by parallel plates) equation
E = V/D
E (electric field strength for radial fields) equation
E = kQ/r²
What is k in electric fields?
8.99E+9 (1/4piEpsilon0)
What do electric field lines show?
The direction of the force acting on a positive charge, and the strength go the field depending on the density of the field lines
What do fields lines look like in a uniform field?
Equally spaced and parallel
Why can use 1/4piEpsilon0 when in air?
Air can be treated as a vacuum when calculating force between charges
Derivation of ΔW= Q ΔV for moving charges between parallel plates
- F = EQ
- d = ΔV/E
- ΔW= F x d = (EQ) x (ΔV/E) = Q ΔV
Path shape of charged particle fired at right angles through an electric field
Parabola (constant force -> constant acceleration)
What is absolute electric potential?
Potential energy per unit charge of a positive point charge at a point in the field
Where is absolute electric potential greatest?
At surface of the charge
Where is absolute electric potential greatest?
At surface of the charge
What is electric potential difference?
Work done needed to move a unit charge between two points
Capacitance equation
Q = CV
Define capacitance
The charge stored by a capacitor per unit potential difference across it
Equation for the dielectric constant
permittivity of medium / permittivity of free space
How do dielectrics work?
- Polar molecules align with their positive side facing the negative plate (and vice versa)
- Producing a counter electric field, reducing the field strength between the places
- The pd V decreases between the capacitor but charge Q remains the same
- So capacitance Q/V increases
What is Coulomb’s law?
Magnitude of the electrostatic force between two point charges in a vacuum is inversely proportional the the product of their charges and inversely proportional to the square of the distances between the charge
Capacitance calculation (using distance between plates etc)?
C = Ae0eR/d
Energy stored by a capacitor
1/2 QV
Capacitor: Area under current time graph
Charge
Capacitor: Gradient of charge time graph
Current
Capacitor: Time to half
ln2 * RC
Capacitor charging : Current-time graph
Start high and then decay
Capacitor charging : Voltage across capacitor-time graph
Start low and then asymptote high
Capacitor charging : Charge-time graph
Start low and then asymptote high
Capacitor discharging : Current-time graph
Start high and then decay
Capacitor discharging : Voltage against both resistor and capacitor-time graph
Start high and then decay
Capacitor discharging : Charge-time graph
Start high and then decay
Capacitance in terms of area and distance between plates
C = A epsilon0 epsilonR / d
When does F=BIL apply?
When current is perpendicular to magnetic field
When does 1T mean?
A force of 1N of 1m of a wire carrying 1A of current perpendicular to a magnetic field
Magnetic fields, what is B?
Magnetic flux density / T
One application of cyclotrons
Producing ion beams for radiotherapy
When does Φ = BA apply?
When B is perpendicular to A
Magnetic flux linkage for coil of wire at an angle
NΦ = BAN cos θ
Magnitude of emf for a rotating coil of wire
EMF = BAN ω sin ωt
What does Faraday’s law state?
The magnitude of induced emf is equal to the rate of change of flux linkage
What does Lenz’s Law state?
The induced emf is in such a direction as to oppose the motion/change the caused it
How to change the scale of Y-axis on oscilloscope
Can select the number of volts per division using the Y-gain control dial
What type of currents do transformers work with?
AC
Transformer equation
Ns/Np = Vs/Vp
What does a step-up transformer do?
Increases the input voltage by having more turns on the secondary coil than the primary
What are by ‘eddy currents’ in transformers? How are they reduced?
- Eddy currents are induced by the alternating magnetic field in the primary coil, and form a loop
- Due to Lenz’s law, they oppose the field that produced them, reducing the field’s flux density
- They also generate heat, which causes energy to be lost through I²R heating
- Eddy current can be reduced by using a laminated iron core, as eddy currents cannot pass through the insulator so their amplitude is reduced
3 causes of inefficiencies in transformers and how to solve these
- Eddy currents / use laminated iron core
- Resistance in coils / Using thick wire, which has a low resistance
- Core not easily magnetised / Use a soft iron core
SI unit for gravitational field strength
N.kg^-1 (not m.s^-2)
Why do orbiting astronauts feel weightless?
- Both astronaut and vehicle have same centripetal acceleration
- And same orbital speed
- So there is no reaction force between astronaut and vehicle
What is the purpose of the iron core in a transformer?
Provides a magnetic path to channel flux, ensuring flux generated by the primary coil is linked to the secondary coil
Explain why an orbiting satellite’s speed doesn’t change even though it is acted on by a force
- The force acts in towards centre of Earth, perpendicular to direction of motion
- There is no movement in the direction of force
- so no work done, so no change in kinetic energy, so no change in speed
What do gravitational field lines show?
The direction of force on a mass
3 features of a low polar orbit
- Orbital period is a few hours
- Earth moves relative to orbit
- Many orbits with different radii and periods are possible
3 advantages of low polar orbit (over geostationary) for monitoring Earth
- Satellite scans the whole surface of Earth
- Gives access to every point on Earth’s surface every day
- Lower signal strength required that that for geostationary satellite
Explain why a magnet Q falling through a copper tubes falls slowly
- Falling magnet means there is a change of flux in the tube
- There is a rate of change of flux, so an emf is induced in the tube
- This emf causes a current
- This current produces a magnetic field
- Lenz’s law means the field opposes the motion of Q (producing an upwards force when Q enters the tube, and again when it leaves the tube)
How do equipotentials cross field lines?
Always at right angles! (Label the right angle if needed)
Similarities between electric fields and gravitational fields
- Both have inverse-square relationships with r
- Both have the concepts of field strength, potential, equipotential surfaces, work done - formulas have the same layout
- Both can be represented using field lines
Key differences between electric and gravitational fields
- Masses always attract
- Charges may repel or attract
- At the subatomic level, gravity can be pretty much ignored, as it is much weaker than the electrostatic force
What is gravity?
The universal attractive force which acts between all matter
Electric field lines always go from _________________ to _________________
Electric field lines always go from positive charge to negative charge (NE positive/negative)
How many time constants until the capacitor can be considered to be fully charged?
5
3 desired features of materials for a moderator in a fission reactor
- small/light nuclei
- should not become radioactive when bombarded with electrons
- available in large amounts
Describe how a transformer works
- A primary coil is wrapped around an iron core
- An alternating current in the coil creates an alternating magnetic field in the core
- The core channels the flux generated in the primary coil, ensuring the primary coil and secondary coil are linked
- The alternating magnetic field induces an emf in secondary coil
- Which creates an alternating current in the secondary coil
Purpose of step-up and step-down transformer in the power grid
step-up: to increase voltage to transport power with minimal energy losses (reduces I²R heating losses)
step-down: to decrease the voltage to save levels for households and buildings
Describe what it would look like if you turned off the time base on an oscilloscope connected to an alternating current
There would be a straight vertical line on the voltage axis
What does it mean for the transformer core to be soft? Why do we want this?
- A magnetically soft material is one that magnetises and demagnetises easily (e.g. magnetisation disappears when current in removed)
- Energy is needed to magnetise and demagnetise the core, and this energy is wasted as it heats the core
- So need to use a magnetically soft material
What is a drawback of increasing the voltage of electricity for power transmission cables?
More insulation/isolation difficulties
