7. Fields and Their Consequences Flashcards
What is the equation for the force between two masses?
F = (G m1 m2) / r^2
What is the equation for gravitational field strength?
g = F / m
What is the equation for the magnitude of gravitational field strength in a radial field?
𝘨 = GM/r²
What is the equation for gravitational potential?
V = - (G m) / r
What is Kepler’s 3rd Law?
T² ∝ R³
How is the escape velocity for gravitational fields calculated?
Vesc = sqrt(2 g R)
What is Vmax?
Largest gravitational potential energy per kg for a given body
The force felt in a force field is non-contact force, True or False?
True
Is force a vector or scalar quantity?
Vector
What are some similarities between electrostatic and gravitational forces?
● Inverse square force laws
● Potential concept
● Equipotential surfaces
● Use of field lines
What are some differences between
electrostatic and gravitational forces?
The gravitational forces from masses always attract, whilst charges may repel or attract.
What is gravity?
Gravity is the universal attractive force which acts between all matter.
What is G?
The universal gravitational constant.
Approx. 6.67x10¯¹¹ m³kg¯¹s¯²
What can field lines tell you about a field?
The direction of the field and the strength of the field depending on the density of the field lines.
What is 𝘨?
𝘨 is the force per unit area in a uniform field
In a radial field the magnitude of 𝘨 is the proportionality constant at that point between force and mass.
𝘨 = GM/r²
What is gravitational potential?
The potential energy per kilogram, at any point in the field. 0 potential is defined at infinity, hence at a point close to a mass the potential of an object would be negative.
What is the work done by moving a mass
in a field?
Mass x change in potential
ΔW = m ΔV
What is the gravitational potential difference?
Gravitational potential difference is the difference in the gravitational potentials of two points in a gravitational field.
What is an equipotential surface?
A surface in which every point on the surface has the same potential.
How much work is done when you move 1km in any direction on an equipotential?
No work is done when moving across equipotentials, as the potential at each point is the same.
Why is gravitational potential a negative value?
Work needs to be done to move an object from the inside the field to outside the field. Since outside the field’s potential is defined as 0 then the potential inside the field must be negative.
What equations could you use to find the speed of an orbiting satellite?
The satellite is in circular motion, so
we would use F = ma with F = GMm / r² rearranged
to a = v² / r = ω² / r. This can be solved to find the
speed (v), angular speed (ω), the radius of the orbit or using T = 2π / ω its time period.
Compare the PE and KE of a lower orbit to a higher one.
A lower orbit has less potential energy and more kinetic energy than a higher orbit.
What is the time period of a geosynchronous orbit?
Geosynchronous orbits have a period of one day.
What symbol represents the permittivity
of free space?
ε₀
When calculating the force between two particles, what can air can be treated as?
A vacuum
For a charged sphere the charge can be assumed to be at what part of the sphere?
The centre
Which is stronger? The gravitational force of subatomic particles or the electrostatic force.
The electrostatic force.
Electric field lines always go from _____
to _____.
Electric field lines always go from positive charge to
negative charge.
What is electric field strength?
The force per unit charge acting at a point in an electric field.
What is the magnitude of E (electric field
strength) in an uniform electric field?
Potential difference between plates (V)/
distance between plates.
What is the trajectory of a particle entering a uniform field at right angles?
It is parabolic.
How is electric potential related to
electric field strength?
E = ΔV/Δr
How is capacitance calculated?
C = Q / V
What is the relative permittivity?
● εr = Q / Q0
● The ratio of the charge stored with the dielectric between the plates to the charge stored when the dielectric is not present.
● The greater the relative permittivity, the greater the capacitance of the capacitor.
What does the area under the graph of charge against pd represent ?
The energy stored by the capacitor.
Describe the Q against t graph for the discharging of a capacitor through a resistor.
1
https://docs.google.com/presentation/d/1XOHaSUe5gTptP0fSHOuiR7zuV0X_Vx3NhKKHEedUO4U/edit?usp=sharing
Describe the V against t graph for the discharging of a capacitor through a resistor.
2
https://docs.google.com/presentation/d/1XOHaSUe5gTptP0fSHOuiR7zuV0X_Vx3NhKKHEedUO4U/edit?usp=sharing
Describe the I against t graph for the discharging of a capacitor through a resistor.
3
https://docs.google.com/presentation/d/1XOHaSUe5gTptP0fSHOuiR7zuV0X_Vx3NhKKHEedUO4U/edit?usp=sharing
Describe the Q against t graph for the charging of a capacitor through a fixed resistor.
4
https://docs.google.com/presentation/d/1XOHaSUe5gTptP0fSHOuiR7zuV0X_Vx3NhKKHEedUO4U/edit?usp=sharing
Describe the V against t graph for the charging of a capacitor through a fixed resistor.
5
https://docs.google.com/presentation/d/1XOHaSUe5gTptP0fSHOuiR7zuV0X_Vx3NhKKHEedUO4U/edit?usp=sharing
What is the time constant?
The time it takes for the charge in a capacitor to fall to 37% of the initial value given by RC (resistance x capacitance).
A capacitor is considered fully discharged after 5 time constants.
How was 37% derived when using the
time constant?
● Start with the formula Q = Q。e^(-t/RC)
● When t = RC (after 1 time constant), the
formula becomes Q = Q。e^(-1)
● e^(-1) ≈ 0.37, which is where 37% came from
What is the half time of a capacitor?
T½ = 0.69RC
What equations do we require for charging a capacitor?
Charging up a capacitor produces
Q = Q。e^(-t/RC)
V = V。e^(-t/RC)
where V。is the battery PD and Q。=CV。
How does a capacitor charge up?
- Electrons move from negative to positive around the circuit.
- The electrons are deposited on plate A, making it negatively charged.
- Electrons travel from plate B to the positive terminal of the battery, giving the plate a positive charge.
- Electrons build up on plate A and an equal amount of electrons are removed from plate B, creating a potential difference across the plates.
- When the p.d across plates = source p.d., the capacitor is fully charged and current stops flowing.
Describe and explain in terms of the movement of electrons how the p.d across a capacitor changes, when it discharges across a resistor.
- Electrons move in opposite direction than when the capacitor was charging up.
- Charge on one plate A decreases as it loses electrons, and plate B gains electrons, neutralising them.
- P.d. decreases exponentially across the plates.
State the 3 expressions for the energy stored by a capacitor.
E = ½ (Q^2/C) = ½ (QV) = ½ (CV^2)
What 2 factors affect the time taken for a capacitor to charge or discharge?
● The capacitance of the capacitor, C. This affects the amount of charge that can be stored by the capacitors at any given potential difference across it.
● The resistance of the circuit, R. This affects the current in the circuit and how quickly it flows, hence how quickly the capacitor charges/discharges.
When a magnetic field is perpendicular to a current-carrying wire, does the wire feel a force ?
Yes, the magnitude of the force is = BIL
L = length of the wire
B = Magnetic flux density
I = Current in the wire
Fleming’s left hand rule for motors represents what properties on what fingers?
Thumb - Thrust/Force
First finger - Field (Magnetic)
Second finger - Current
What is magnetic flux density (B)?
Flux density measured in Tesla (T) or
Webers/meters² (Wb/m²), is the flux per
metre².
A charged particle moving through a field
feels a force when it is traveling along
the field lines or perpendicular to them?
Perpendicular to the field.
What is the equation for the Force felt by
a moving charge in a magnetic field ?
F = BQv
Is the force applied to the particles applied perpendicular to the particles motion or in one direction?
Perpendicular to its motion, causing it to move in a circular motion.
Which fields do cyclotrons use? A. Electric field B. Magnetic field C. Gravitational field D. Both Electric and Magnetic
D. An electric field and a magnetic field.
How does a Cyclotron work and what’s the electric and magnetic fields purpose in a cyclotron?
A cyclotron is made up of 2 semicircular electrodes called “Dees” with a magnetic field applied perpendicular to the Dees and an alternating pd applied between the Dees.
Each Dee is a metal electrodes with opposite charges, this creates an electric field in the gap between the two Dees. This is what accelerates the particles.
The magnetic field causes the particles to move in a circular motion, which allows it to gain speed whilst minimising space. As they speed up the radius of their motion increases, until it breaks free tangential to one of the Dees.
What is magnetic flux? (Quantitative)
Φ = BA
Flux = Flux Density x Area
Where B is normal to A.
What is flux linkage?
NΦ = The number of turns cutting the flux at one time.
What is the flux linkage of a rectangular coil rotating through a magnetic field?
NΦ = BANcosΘ
What is Faraday’s Law?
The induced e.m.f. is directly proportional to the rate of change of magnetic flux linkage.
What is Lenz’s Law?
The direction of the induced e.m.f. is such as to oppose the change that induces it. 𝜀 = -𝑁 (ΔФ)/(Δt)
What happens when you move a straight conductor through a magnetic field?
The electrons experience a force pushing them to one end of the conductor creating an emf across the conductor. The rod obeys Faraday’s law, it is changing flux as it moves through the field hence an EMF is induced.
What would be the EMF produced when
rotating a coil at a constant rate in a
magnetic field?
𝜀 = BAN⍵sin(⍵t)
Where ⍵ is the angular velocity of the rotating
coil.
Describe how one would use an oscilloscope
Oscilloscopes are used to displace AC waves, the x axis is called the time base and shows how long it takes the wave to move 1 division and the y axis shows how much PD is needed to move the wave up 1 division. Using this we find the peak voltage, time period and frequency.
How does a transformer work?
A primary coil wrapped around an iron core with an alternating p.d. creates an alternating magnetic field, this magnetic field induces an EMF in a secondary coil also wrapped around the core. This creates a current in the secondary coil.
What kind of current is produced by a transformer and why?
An alternating current.
An EMF is induced by a changing magnetic field, hence the EMF induced is alternating producing an alternating current.
Why are transformers used?
By changing the number of coils, the transformers can be used to increase the voltage and reduce current when transporting power, with minimal energy loses. The voltage is then dropped again locally to ensure safe usage in households.
What equation links the number of coils
in a transformer with their voltages?
Ns / Np = Vs / Vp
What is transformer efficiency?
The ratio of output power in the transformer to input power.
= IsVs / IpVp
In a step-up transformer, does the secondary coil or primary coil have more coils?
The secondary coil.
Step-up transformers increase the voltage, hence more coils need to be in the secondary coil for a larger p.d.
What is an eddy current?
As the primary coils magnetic field induces emf in the secondary coil, it also induces emf and hence mini currents within the iron core.These are known as eddy currents.
Why are eddy currents a problem?
By Lenz’s law the emf created and its field opposes that of the primary coil. This causes energy loss via resistive heating of the iron core by the eddy currents, which reduces efficiency.
How can you reduce eddy current losses?
Use a laminated iron core. Thin sheets of iron with an electrical insulator in between, which reduces the eddy currents circuit.
