1
Q
What is gravity?
A
Gravity is a universal attractive force that acts between all of matter.
2
Q
What are gravitational fields?
A
Regions in which a body would experience a non-contact force
3
Q
What do the gravitational field lines represent?
A
They show the direction of a force on a mass placed in the field (always towards the object).
The strength of the field is represented by the density of the field lines (more dense means stronger).
4
Q
What is Newton’s law of gravitation?
A
F = Gm1m2 / r2
where
F is gravitational force (N)
G is the gravitational constant (6.67 x 10-11 Nm2kg-2 - BU: m3kg-1s-2)
m1 is the mass of the first object (kg)
m2 is the mass of the second object (kg)
r is the distance between the objects (m)
5
Q
How to calculate gravitational field strength?
A
g = F/m = GM / r2
where
g is the gravitational field strength (N/kg)
G is constant of gravitation
M is the mass of the larger object (e.g. planet)
r is the radius of the large object
6
Q
What is gravitational potential?
A
The work done in bringing a 1kg mass from infinity to a point.
Therefore, the gravitational potential at infinity is 0 and gravitational potential is negative.
7
Q
What are equipotential surfaces?
A
The gravitational potential is constant along an equipotential surface.
Field lines are perpendicular to equipotentials.
Closer that the lines are, the stronger the gravitational acceleration.
No work is done moving along an equipotential surface.
8
Q
What is the area under the graph of gravitational force and distance between objects?
A
The work done.
9
Q
What does the area under the gravitational field strength and distance between objects represent?
A
The change in gravitational potential.
g = - ΔV/Δr
- therefore, g is also the gradient of the V against r graph
10
Q
How to calculate the kinetic energy of a satellite?
A
KE = 1/2 GMm/r
where
KE is the kinetic energy (J)
G is the constant of gravitation
M is larger mass
m is the smaller mass
r is the distance between the objects
11
Q
How to find the orbital period and speed of planets and satellites?
A
V = 2πr / T = √GM/r
Where
r is the radius of orbit (m)
T is the time period of orbit (s)
V is the orbital speed (rad/s)
G is the constant of gravitation
M is the mass of the planet which is being orbitted
12
Q
How to prove that T^2 is proportional to r^3 in orbit (where T is the orbit time period and r is the distance between satellite and planet)?
A
1) Set gravitational force as equal to centripetal force:
GMm / r2 = m⍵2r
2) Rearrange with ⍵ = 2π/T:
GM / r3 = 4π2 / T2
3) Since everything else is constant, T squared and r cubed are proportional.
13
Q
How to find the total energy of an orbiting satellite?
A
ET = 1/2 mv2 - GMm/r
If total energy is 0J, then the satellite has escaped the orbit. Therefore, we can calculate escape velocity using:
vescape = √2GM/r
14
Q
What is a geostationary orbit?
A
A satellite which has a geostationary orbit, it has a 24 hours, equatorial orbit moving from west to east.
15
Q
What are the uses of geostationary orbits?
A
- Communication
- Reconnaisance
- GPS
16
Q
How to work out the height of a geostationary orbit?
A
r = 3√T2GM/4π2
- this gives height from centre of planet so subtract radius of planet
17
Q
What are the properties of the graph of log(T) against log(R)?
A
log(T) = (3/2)log(r) + (1/2)(log(4π2/GM)
- therefore, the gradient is always 3/2
- the y-intercept is always (1/2)(log(4π2/GM)
18
Q
What is Newton’s law of gravitation in words?
A
The gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of their separation.
19
Q
What is Coulomb’s Law in words?
A
The electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of their separation.
20
Q
What is the equation for electrostatic force between two charges?
A
F = Q1Q2 / 4πε0r2
where
Q1 is charge of one object
Q1 is the charge of the other object
ε0 is the permittivity of free space
r is the distance between the centres of the charges
21
Q
What do negative and positive forces mean for electrostatic forces?
A
Negative is attraction, positive is repulsion
22
Q
What are the approximations used in Coulomb’s law?
A
- Air is treated as a vacuum
- Charge of sphere is considered to be a point charge at its centre
- Uniform spherical conductor is one where its charge is distributed evenly
- Electric field lines around a spherical conductor are therefore identical to those around a point charge
- Field lines are radial and direction depends on charges
- Field lines away from centre if object is positively charged
23
Q
What are the rules for electric field lines?
A
- Field lines represent magnitude and direction of field
- Always from positive to negative
- In uniform field, all lines equally spaced so constant electric field strength and force on test charge has same magnitude and direction at all points in field
- For radial field:
- Lines spread out with distance
- Equally spaced as they exit surface of charge
- Separation increases with distance so field strength decreases
- Field lines must never cross
24
Q
What is electric field strength?
A
The force per unit charge experience by a small positive charge placed at that point in the electric field
E = F/Q
25
What is the equation for electric field strength in a uniform electric field?
E = V/d
E can be Vm-1 or NC-1
26
What is the electric field strength equation of a point charge?
E = F/q = Q/4πε0r2
27
What is the motion of a charged particle in an electric field?
A charged particle in an electric field will experience a force on it that will cause it to move. If stationary, it will move parallel to field lines else it will have a **parabolic trajectory**.
28
What determines the direction of motion of a charge in an electric field?
The charge ( +ve or -ve )
29
What factors affect the amount of deflection in an electric field of a charged particle?
- Mass (greater mass means smaller deflection)
- Charge (greater charge, greater resultant force, greater deflection)
- Speed (greater speed, smaller deflection)
30
How do you combine electric fields at a point?
Add the vectors of the electric fields acting at that point.
31
What are the similarities between gravitational and electrostatic fields?
- Field lines around a point mass and a **negative** point charge are identical
- Field lines in **uniform** gravitational fields and electric fields are identical
- Both forces follow **inverse square law** relationships with **distance**
- Both gravitational potential and electric potential follow an inverse relationship with distance
- Equipotential surfaces are **spherical** around a point mass or charge and equally spaced parallel lines in uniform fields
32
What are the differences between gravitational and electrostatic fields?
- Gravitational forces are proportional to the product of **masses** for each particle whilst electrostatic force is proportional to the the product of the **charges** for each particle
- Gravitational force is **always attractive** whilst electrostatic force can be **attractive** or **repulsive**
- Gravitational potential is **always negative** whilst electric potential can be either **negative** or **positive**
- Both forces are calculated using **different constants of proportionality** with gravitational forces calculated with the gravitational constant G and electrostatic forces having the Coulomb constant k as its constant of proportionality
33
What is electric potential?
*The work done per unit charge in taking a small positive test charge from infinity to a defined point in an electric field.*
- units of JC-1 or V
- scalar quantity but positive or negative to indicate sign of charge
- zero at infinity
34
What is electric potential in a radial field?
*V = Q / 4πε0r*
Where
V = electric potential (V)
Q = magnitude of the charge producing the potential (C)
r = distance from the centre of the point charge
35
How does electric potential change as we move around objects of different charges?
Positive:
- potential **increases** as separation **decreases**
- energy must be supplied to a positive test charge to overcome the repulsive force
Negative:
- potential **increases** as separation **increases**
- energy is released as a positive test charge moves in direction of attractive force
36
What is the features of an electric potential graph?
- If charge causing field is **positive**, all potential values are **positive**
- If charge causing field is **negative**, all potential values are **negative**
- As r increases, V against r follows a 1/r relationship
- The **gradient** of the graph at any point is equal to the **field strength at that point in the field**
37
What is the relationships between electrostatic force, electric potential energy, electric potential and electric field strength
38
What is the work done on a charge that moves through an electric field?
*ΔW = qΔV*
Where
W = work done (J)
q = magnitude of charge moving in the field (C)
ΔV = potential difference between two points (JC-1)
39
How are equipotential lines and surfaces represented in diagrams?
Dotted lines which are perpendicular to the electric field linees in both radial and uniform fields.
- They get further apart in radial fields
40
What are capacitors and what is their circuit symbol?
Capacitors are electrical devices used to store electric potential energy in electronic circuits (commonly for backup release of energy).
- Circuit symbol is two parallel lines (similar to cell but both lines same length)
41
What is capacitance?
*The charge stored per unit potential difference between the plates of a capacitor.*
- The greater the **capacitance**, greater the **energy stored** in the capacitor
42
What is the equation for capacitance?
*C = Q / V*
Where
C = capacitance measured in Farads (F)
Q = charge (C)
V = potential difference between plates (V)
43
How does the dielectric material in a capacitor work?
- The dielectric material is made of many polar molecules
- These molecules have a *postive* and *negative* pole
- When **no charge** is applied to the capacitor, there is no **electric field** between the parallel plates and molecules are aligned in **random** directions
- Once **charge is applied**, one parallel plate becomes **positive** and the other **negative**
- This causes an **electric field** to occur between the plates
- The **negative poles** of the polar molecules are attracted tot the **positive plate** and the **positive poles** are attracted to the **negative plate**
- Hence, the molecules experience a **rotational force** which causes them to align themselves **parallel to the field**
- Hence, their **electric field** combines with the **electric field between the plates** which causes an overall **lower potential difference**
- Since C = Q / V and V has decreased, capacitance increases
44
What is relative permittivity?
*The ratio of permittivity of a material to the permittivity of free space*
εr = ε / ε0
Where
εr = relative permittivity (**no units**)
ε = permittivity of material (Fm-1)
ε0 = permittivity of free space (Fm-1)
45
What is the alternate equation for capacitance to do with the dielectric material?
*C = Aε0εr/d*
Where
C = capacitance (F)
A = cross-sectional area of the plates (m2)
d = separation of the plates (m)
ε0 = permittivity of free space (Fm-1)
εr = relative permittivity of dielectric material
46
What happens when a capacitor when it is charged?
- Power supply pushes electrons onto the negative plate and pulls them from the postive plate
- Work is done on the electrons and **electrical energy** becomes stored on the plates
- Charge Q on the capacitor is **directly proportional** to its potential difference V since capacitance remains constant
- **Area under the charge-p.d.** is the electric potential energy stored
47
What is the equation for energy stored in a capacitor?
*E = (1/2) Q V*
Where
E = work done or energy stored (J)
Q = charge (C)
V = potential difference (V)
Equivalent equations:
*E = 1/2 CV2* and *E = 1/2 Q2/C*
Where
C = capacitance (F)
48
Explain how the p.d. - current graph changes as a capacitor is charged.
- Initially, when the potential difference is small, there are few free electrons on the negative plate of the capacitor
- Therefore, electrons are able to be pushed onto the negative plate from the negative terminal of the power supply since there is a low resistive force
- As electrons accumulate and the p.d. increases, the repulsive force from the accumulated increases and the rate of charge being pushed onto the negative plate decreases
- Hence, the **current decreases** as the **potential difference increases**
49
What are the key features of the charging graphs?
- Shapes of **p.d.** and **charge** against time graphs are identical
- **Current** against time is an exponential decay curve
- The initial value of the current starts on the y-axis and decreases exponentially
- The intial value of the p.d. and charge starts at 0 up to a maximum value
50
What are the key features of discharging curves?
- Discharged through a resistor with no power supply present
- Shape of current, p.d. and charge against time graphs are identical
- Each graph shows **exponential decay** curves with **decreasing gradient**
- The intial values start on y-axis and decrease exponentially
- The rate of discharge depends on the **resistance** of the circuit
51
What is the time constant of a capacitor?
*The time taken for the charge, current or voltage of a discharging capacitor to decrease to 1/e of its original value.*
tau = RC
Where
tau = time constant (s)
R = resistance of the resistor (Ω)
C = capacitance of the capacitor (F)
52
What are the discharging equations of a capacitor?
*V = V0e-t/RC*
*I = I0e-t/RC*
*Q = Q0e-t/RC*
Where
V is the voltage across the capacitor at time t
I is the current
Q is the charge
V0 is the initial voltage
Q0 is the initial charge
R is the resistance of the resistor
C is the capacitance of the capacitor
53
What are the charging equations of a capacitor?
Initial voltage / charge / current - discharging equation
54
Why are satellites launched from the equator?
At this position, the satellite has the largest initial speed / kinetic energy from the Earth’s rotation.
55
What is the equation relating orbital radius and time period?
T2 is proportional to r3
T2 = 4π2r3 / GM
56
What is a magnetic field?
A region of space in which a **magnetic pole** will experience a **force**.
57
What can create a magnetic field?
- A **moving** electric charge
- A permanent magnet
58
What is the magnetic flux density of a magnetic field?
The number of magnetic flux lines passing through a region of space per unit area.
- Measured in Teslas (T)
- denoted as B
59
What does a magnetic flux density of 1T mean?
The flux density of a field that causes a 1N force on a current-carrying wire which carries a current of 1A at right angles to the flux.
60
How do you draw magentic fields?
- Field lines from north pole to south pole
- Use arrows to indicate direction
- Flux lines are drawn closer together where the field strength is greater
61
What is the equation for the magnetic force on a current-carrying wire?
*F = BILcosθ*
where
F is the force exerted on the wire (N)
I is the current through the wire (A)
L is the length of the wire in the field (m)
θ is the angle between the normal to the conductor and the applied B field
62
What is Fleming's left hand rule?
FBI with F being thumb
63
What is the equation for the magnetic force on a moving charge?
*F = BQvsinθ*
where
F = force on charge (N)
B = magnetic flux density (T)
Q = charge (Q)
v = speed of the charge (ms-1)
θ = angle between charge and flux lines
64
How do you use FLHR to find direction of force on a moving charge?
- Positive : current same direction as motion of charge
- Negative: current in opposite direction as motion of charge
65
What happens when a charged particle enters a uniform magnetic field?
- The particle travels in a circular path
- Radius of path determined by force on it
*mv2 / r = BQv*
so
*r = mv / BQ*
66
What does the equation for radius of motion in a magnetic field for a charge suggest?
- Higher speed means larger radius
- Higher mass means larger radius
- Greater magnetic flux density means smaller radius
- Greater charge means smaller radius
67
What happens inside a dee of a cyclotron particle accelerator?
- A **uniform** magnetic field is applied perpendicular to the path of the particles inside the dees
- The force exerted on these particles acts as the centripetal force for their motion within the dee
- This causes the particles to move in a circular path when inside the dees
68
What happens to particles crossing the gap between dees of a particle accelerator?
- An electric field is applied on the particles in the gap
- This causes the particles to accelerate to a greater speed before they enter the next dee
- The particles with have a greater radius for their circular path in their next dee since their speed is greater
69
What happens as charged particles in a cyclotron particle accelerator leave the dees.
- The charged particles travel with constant speed in the dees
- This means the time spent in one dee is constant
- The direction of the electric field **alternates each time** the particles reach a gap
- This means they will always **accelerate towards the opposite dee**
- This process repeats as the particles spiral outwards until they leave the cyclotron at the desired speed
70
What is the role of the uniform magnetic field in a cyclotron particle accelerator?
To supply the centripetal force required to keep the charged particles travelling in circular motion
71
What is the role of the electric field in a cyclotron particle accelerator?
To accelerate the charged particles between the dees
- the particles gain additional energy (QV)
- move faster / with a greater radius in the next dee
72
What are the uses of cyclotrons?
- To produce tracers for imaging
- Create high-energy beams of radiation for radiotherapy
73
What occurs in electromagnetic induction?
An e.m.f. is induced in a conductor due to changes in magnetic flux
- Direction of a magnetic field through a coil changes
- Conductor cuts through magnetic field lines
74
What determines the emf induced in electromagnetic induction?
The magnetic flux (total magnetic field that passes through a given area)
75
What is the mathematical definition of magnetic flux?
*Φ = BA*
or
*The product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density.*
where
Φ = magnetic flux (Wb)
B = magnetic flux density (T)
A = cross-sectional area (m2
76
What is the mathematical definition of magnetic flux linkage?
*ΦN = BANcosθ*
or
*The product of the magnetic flux and the number of turns of the coil.*
where
ΦN = magnetic flux linkage (Wb turns)
B = magnetic flux density (T)
A = cross-sectional area (m2)
N = number of turns of the coil
θ = angle between the magnetic field lines and the perpendicular to the plane of the area (the normal line)
77
What are the uses of electromagnetic induction?
- Electrical generators : convert mechanical energy to electrical energy
- Transformers : used in electrical power transmission
78
What is the expected results in the magnet through a coil experiment?
-When magnet stationary, voltmeter shows 0 reading (no rate of change of flux, no emf induced)
- When magnet moves inside coils, reading on voltmeter (field lines cut through coil, so change in magnetic flux, so induced emf)
- When taken back out of coil, emf induced in the opposite direction
79
What happens when speed of magnet in coil increases?
- Induces an emf with a higher magnitude
80
What factors affect magnitude of induced emf?
- Moving magnet faster through coil
- Adding more turns to coil
- Increasing the strength of bar magnet
81
What is Faraday's law?
The magnitude of the induced emf is directly proportional to the rate of change in magnetic flux linkage
82
What is Lenz's law?
The induced emf acts in such a direction to produce effects that oppose the change causing it
83
What is the equation for induced emf?
*ε = -NΔΦ/Δt*
where
ε = induced e.m.f. (V)
N = number of turns of coil
ΔΦ = change in magnetic flux (Wb)
Δt = time interval (s)
84
What is the equation for the flux linkage of a rotating coil?
*ΦN = BANcosωt*
where
ω = angular speed of the coil
t = time (s)
85
What is the equation for induced emf in a rotating coil?
*ε = BANωsinωt*
where
ω = angular speed of the coil
t = time (s)
out of phase by π/2 with flux linkage
86
How to read an oscilloscope?
- Time-base settings tell how much one horizontal square is
- Y-gain settings indicate volts per vertical square
- Peak voltage is greatest height above equilibrium
- Peak-to-peak voltage is double the peak voltage
87
How to find Vrms from peak voltage?
*Vrms = Vpeak / √2*
88
What is the equation for electrical power of an AC current?
*P = IrmsVrms*
89
What is a transformer and why is it used?
- Device that changes high **alternating** voltage at a low current to a low **alternating** voltage to a high current and vice versa
- Used to reduce heat energy lost whilst electricity is transmitted down electrical power lines from power stations to the national grid
90
Why is a soft iron core needed in a tranformer?
- Focuses and directs the magnetic field from the primary to the secondary coil
- Soft iron used because it can be easily magnetised and demagnetised
91
How is an emf induced in the secondary coil in a transformer?
- In the primary coil, an alternating current producing an alternating voltage is applied
- This creates an alternating magnetic field inside the iron core and therefore a changing magnetic flux linkage
- A changing magnetic field passes through to the secondary coil through the iron core
- This results in a changing magnetic flux linkage in the secondary coil and from Faraday's Law, an e.m.f is induced
92
What is the transformer equation?
*Ns / Np = Vs / Vp*
where
N is number of turns in the coils
V is the voltages
93
What are step-up and step-down transformers?
- Step-up : increases voltage, used between power stations and transmission wires
- Step-down : decreases voltage, used between transmission wires and buildings
94
What is the transformer efficiency equation?
*Efficiency = IsVs / IpVp*
where efficiency is a decimal less than 1
95
Why are transformers not 100% efficient?
- **Eddy currents** is where an **emf** is induced in the **soft iron core** due to the changing magnetic field of the alternating current in the primary coil
- The current dissipates energy by generating heat in the wires
96
How are Eddy currents reduced?
- **Laminating** the iron core with layers of insultation, so current can't flow between them
- Making the core with a material of a high resistivity
97
What are the causes of inefficiencies in the coils of the wire of a transformer?
- Coils have resistance
- Heat energy loss from current flowing through coils
- Larger current, larger heat loss
98
What are the causes of inefficiencies in the soft iron core of a transformers?
- Induced eddy currents
- Reversal of magnetism
- Poor insulation between primary and secondary coil
99
What ways can energy loss in a transformer be reduced?
- Making core from soft iron or iron alloys to allow easy magnetisation and demagnetisation
- Laminating the core
- Using thick wires, especially in secondary coil of step-down transformers
- Use a core that allows all the flux due to the first coil to be linked to the secondary coil
100
How is energy loss due to heating reduced?
- Step-up transformers to increase voltage and decrease current
- P = I2R
- Doubling current means doubling the energy loss
101
- A not D because field lines need to perpendicular to surface as they approach it
102
What are conditions for Charles' law?
- constant pressure
- closed system / fixed number of gas molecules
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