A-level Physics₇₄₀₈

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3.7 Fields and their consequences (A-level only)

The concept of field is one of the great unifying ideas in physics. The ideas of gravitation, electrostatics and magnetic field theory are developed within the topic to emphasise this unification. Many ideas from mechanics and electricity from earlier in the course support this and are further developed. Practical applications considered include: planetary and satellite orbits, capacitance and capacitors, their charge and discharge through resistors, and electromagnetic induction. These topics have considerable impact on modern society.

3.7.1 Fields (A-level only)

Content	Opportunities for skills development
Concept of a force field as a region in which a body experiences a non-contact force. Students should recognise that a force field can be represented as a vector, the direction of which must be determined by inspection. Force fields arise from the interaction of mass, of static charge, and between moving charges. Similarities and differences between gravitational and electrostatic forces: Similarities: Both have inverse-square force laws that have many characteristics in common, eg use of field lines, use of potential concept, equipotential surfaces etc Differences: masses always attract, but charges may attract or repel

Content

Opportunities for skills development

Concept of a force field as a region in which a body experiences a non-contact force.

Students should recognise that a force field can be represented as a vector, the direction of which must be determined by inspection.

Force fields arise from the interaction of mass, of static charge, and between moving charges.

Similarities and differences between gravitational and electrostatic forces:

Similarities: Both have inverse-square force laws that have many characteristics in common, eg use of field lines, use of potential concept, equipotential surfaces etc

Differences: masses always attract, but charges may attract or repel

3.7.2 Gravitational fields (A-level only)

3.7.2.1 Newton's law (A-level only)

Content	Opportunities for skills development
Gravity as a universal attractive force acting between all matter. Magnitude of force between point masses: $F = \frac{G m_{1} m_{2}}{r^{2}}$ where $G$ is the gravitational constant.	MS 0.4 Students can estimate the gravitational force between a variety of objects.

Content

Opportunities for skills development

Gravity as a universal attractive force acting between all matter.

Magnitude of force between point masses: $F = \frac{G m_{1} m_{2}}{r^{2}}$ where $G$ is the gravitational constant.

MS 0.4

Students can estimate the gravitational force between a variety of objects.

3.7.2.2 Gravitational field strength (A-level only)

Content	Opportunities for skills development
Representation of a gravitational field by gravitational field lines. $g$ as force per unit mass as defined by $g = \frac{F}{m}$ Magnitude of $g$ in a radial field given by $g = \frac{G M}{r^{2}}$

Content

Opportunities for skills development

Representation of a gravitational field by gravitational field lines.

$g$ as force per unit mass as defined by $g = \frac{F}{m}$

Magnitude of $g$ in a radial field given by $g = \frac{G M}{r^{2}}$

3.7.2.3 Gravitational potential (A-level only)

Content	Opportunities for skills development
Understanding of definition of gravitational potential, including zero value at infinity. Understanding of gravitational potential difference. Work done in moving mass $m$ given by $∆ W = m ∆ V$ Equipotential surfaces. Idea that no work is done when moving along an equipotential surface. $V$ in a radial field given by $V = - \frac{G M}{r}$ Significance of the negative sign. Graphical representations of variations of $g$ and $V$ with $r$ . $V$ related to $g$ by: $g = - \frac{∆ V}{∆ r}$ $∆ V$ from area under graph of $g$ against $r$ .	MS 3.8, 3.9 Students use graphical representations to investigate relationships between $v$ , $r$ and $g$ .

Content

Opportunities for skills development

Understanding of definition of gravitational potential, including zero value at infinity.

Understanding of gravitational potential difference.

Work done in moving mass $m$ given by $∆ W = m ∆ V$

Equipotential surfaces.

Idea that no work is done when moving along an equipotential surface.

$V$ in a radial field given by $V = - \frac{G M}{r}$

Significance of the negative sign.

Graphical representations of variations of $g$ and $V$ with $r$ .

$V$ related to $g$ by: $g = - \frac{∆ V}{∆ r}$

$∆ V$ from area under graph of $g$ against $r$ .

MS 3.8, 3.9

Students use graphical representations to investigate relationships between $v$ , $r$ and $g$ .

3.7.2.4 Orbits of planets and satellites (A-level only)

Content	Opportunities for skills development
Orbital period and speed related to radius of circular orbit; derivation of $T^{2} \propto r^{3}$ Energy considerations for an orbiting satellite. Total energy of an orbiting satellite. Escape velocity. Synchronous orbits. Use of satellites in low orbits and geostationary orbits, to include plane and radius of geostationary orbit.	MS 0.4 Estimate various parameters of planetary orbits, eg kinetic energy of a planet in orbit. MS 3.11 Use logarithmic plots to show relationships between $T$ and $r$ for given data.

Content

Opportunities for skills development

Orbital period and speed related to radius of circular orbit; derivation of $T^{2} \propto r^{3}$

Energy considerations for an orbiting satellite.

Total energy of an orbiting satellite.

Escape velocity.

Synchronous orbits.

Use of satellites in low orbits and geostationary orbits, to include plane and radius of geostationary orbit.

MS 0.4

Estimate various parameters of planetary orbits, eg kinetic energy of a planet in orbit.

MS 3.11

Use logarithmic plots to show relationships between $T$ and $r$ for given data.

3.7.3 Electric fields (A-level only)

3.7.3.1 Coulomb's law (A-level only)

Content	Opportunities for skills development
Force between point charges in a vacuum: $F = \frac{1}{4 π ε_{0}} \frac{Q_{1} Q_{2}}{r^{2}}$ Permittivity of free space, $ε_{0}$ Appreciation that air can be treated as a vacuum when calculating force between charges. For a charged sphere, charge may be considered to be at the centre. Comparison of magnitude of gravitational and electrostatic forces between subatomic particles.	MS 0.3, 2.3 Students can estimate the magnitude of the electrostatic force between various charge configurations.

Content

Opportunities for skills development

Force between point charges in a vacuum:

$F = \frac{1}{4 π ε_{0}} \frac{Q_{1} Q_{2}}{r^{2}}$

Permittivity of free space, $ε_{0}$

Appreciation that air can be treated as a vacuum when calculating force between charges.

For a charged sphere, charge may be considered to be at the centre.

Comparison of magnitude of gravitational and electrostatic forces between subatomic particles.

MS 0.3, 2.3

Students can estimate the magnitude of the electrostatic force between various charge configurations.

3.7.3.2 Electric field strength (A-level only)

Content	Opportunities for skills development
Representation of electric fields by electric field lines. Electric field strength. $E$ as force per unit charge defined by $E = \frac{F}{Q}$ Magnitude of $E$ in a uniform field given by $E = \frac{V}{d}$ Derivation from work done moving charge between plates: $F d = Q Δ V$ Trajectory of moving charged particle entering a uniform electric field initially at right angles. Magnitude of $E$ in a radial field given by $E = \frac{1}{4 π ε_{0}} \frac{Q}{r^{2}}$	PS 1.2, 2.2 / AT b Students can investigate the patterns of various field configurations using conducting paper (2D) or electrolytic tank (3D).

Content

Opportunities for skills development

Representation of electric fields by electric field lines.

Electric field strength.

$E$ as force per unit charge defined by $E = \frac{F}{Q}$

Magnitude of $E$ in a uniform field given by $E = \frac{V}{d}$

Derivation from work done moving charge between plates: $F d = Q Δ V$

Trajectory of moving charged particle entering a uniform electric field initially at right angles.

Magnitude of $E$ in a radial field given by $E = \frac{1}{4 π ε_{0}} \frac{Q}{r^{2}}$

PS 1.2, 2.2 / AT b

Students can investigate the patterns of various field configurations using conducting paper (2D) or electrolytic tank (3D).

3.7.3.3 Electric potential (A-level only)

Content	Opportunities for skills development
Understanding of definition of absolute electric potential, including zero value at infinity, and of electric potential difference. Work done in moving charge $Q$ given by $∆ W = Q ∆ V$ Equipotential surfaces. No work done moving charge along an equipotential surface. Magnitude of $V$ in a radial field given by $V = \frac{1}{4 π ε_{0}} \frac{Q}{r}$ Graphical representations of variations of $E$ and $V$ with $r$ . $V$ related to $E$ by $E = \frac{∆ V}{∆ r}$ $∆ V$ from the area under graph of $E$ against $r$ .

Content

Opportunities for skills development

Understanding of definition of absolute electric potential, including zero value at infinity, and of electric potential difference.

Work done in moving charge $Q$ given by $∆ W = Q ∆ V$

Equipotential surfaces.

No work done moving charge along an equipotential surface.

Magnitude of $V$ in a radial field given by $V = \frac{1}{4 π ε_{0}} \frac{Q}{r}$

Graphical representations of variations of $E$ and $V$ with $r$ .

$V$ related to $E$ by $E = \frac{∆ V}{∆ r}$

$∆ V$ from the area under graph of $E$ against $r$ .

3.7.4 Capacitance (A-level only)

3.7.4.1 Capacitance (A-level only)

Content	Opportunities for skills development
Definition of capacitance: $C = \frac{Q}{V}$

3.7.4.2 Parallel plate capacitor (A-level only)

Content	Opportunities for skills development
Dielectric action in a capacitor $C = \frac{A ε_{0} ε_{r}}{d}$ Relative permittivity and dielectric constant. Students should be able to describe the action of a simple polar molecule that rotates in the presence of an electric field.	PS 1.2, 2.2, 4.3 / AT f, g Determine the relative permittivity of a dielectric using a parallel-plate capacitor. Investigate the relationship between $C$ and the dimensions of a parallel-plate capacitor eg using a capacitance meter.

Content

Opportunities for skills development

Dielectric action in a capacitor $C = \frac{A ε_{0} ε_{r}}{d}$

Relative permittivity and dielectric constant.

Students should be able to describe the action of a simple polar molecule that rotates in the presence of an electric field.

PS 1.2, 2.2, 4.3 / AT f, g

Determine the relative permittivity of a dielectric using a parallel-plate capacitor.

Investigate the relationship between $C$ and the dimensions of a parallel-plate capacitor eg using a capacitance meter.

3.7.4.3 Energy stored by a capacitor (A-level only)

Content	Opportunities for skills development
Interpretation of the area under a graph of charge against pd. $E = \frac{1}{2} Q V = \frac{1}{2} C V^{2} = \frac{1}{2} \frac{Q^{2}}{C}$

Content

Opportunities for skills development

Interpretation of the area under a graph of charge against pd.

$E = \frac{1}{2} Q V = \frac{1}{2} C V^{2} = \frac{1}{2} \frac{Q^{2}}{C}$

3.7.4.4 Capacitor charge and discharge (A-level only)

Content	Opportunities for skills development
Graphical representation of charging and discharging of capacitors through resistors. Corresponding graphs for $Q$ , $V$ and $I$ against time for charging and discharging. Interpretation of gradients and areas under graphs where appropriate. Time constant $R C$ . Calculation of time constants including their determination from graphical data. Time to halve, $T_{½} = 0.69 R C$ Quantitative treatment of capacitor discharge, $Q = Q_{0} e^{- \frac{t}{R C}}$ Use of the corresponding equations for $V$ and $I$ . Quantitative treatment of capacitor charge, $Q = Q_{0} (1 - e^{- \frac{t}{R C}})$
Required practical 9: Investigation of the charge and discharge of capacitors. Analysis techniques should include log-linear plotting leading to a determination of the time constant, $R C$	MS 3.8, 3.10, 3.11 / PS 2.2, 2.3 / AT f, k

Content

Opportunities for skills development

Graphical representation of charging and discharging of capacitors through resistors. Corresponding graphs for $Q$ , $V$ and $I$ against time for charging and discharging.

Interpretation of gradients and areas under graphs where appropriate.

Time constant $R C$ .

Calculation of time constants including their determination from graphical data.

Time to halve, $T_{½} = 0.69 R C$

Quantitative treatment of capacitor discharge, $Q = Q_{0} e^{- \frac{t}{R C}}$

Use of the corresponding equations for $V$ and $I$ .

Quantitative treatment of capacitor charge, $Q = Q_{0} (1 - e^{- \frac{t}{R C}})$

Required practical 9: Investigation of the charge and discharge of capacitors. Analysis techniques should include log-linear plotting leading to a determination of the time constant, $R C$

MS 3.8, 3.10, 3.11 / PS 2.2, 2.3 / AT f, k

3.7.5 Magnetic fields (A-level only)

3.7.5.1 Magnetic flux density (A-level only)

Content	Opportunities for skills development
Force on a current-carrying wire in a magnetic field: $F = B I l$ when field is perpendicular to current. Fleming’s left hand rule. Magnetic flux density $B$ and definition of the tesla.
Required practical 10: Investigate how the force on a wire varies with flux density, current and length of wire using a top pan balance.

Content

Opportunities for skills development

Force on a current-carrying wire in a magnetic field: $F = B I l$ when field is perpendicular to current.

Fleming’s left hand rule.

Magnetic flux density $B$ and definition of the tesla.

Required practical 10: Investigate how the force on a wire varies with flux density, current and length of wire using a top pan balance.

3.7.5.2 Moving charges in a magnetic field (A-level only)

Content	Opportunities for skills development
Force on charged particles moving in a magnetic field, $F = B Q v$ when the field is perpendicular to velocity. Direction of force on positive and negative charged particles. Circular path of particles; application in devices such as the cyclotron.	MS 4.3 Convert between 2D representations and 3D situations.

Content

Opportunities for skills development

Force on charged particles moving in a magnetic field, $F = B Q v$ when the field is perpendicular to velocity.

Direction of force on positive and negative charged particles.

Circular path of particles; application in devices such as the cyclotron.

MS 4.3

Convert between 2D representations and 3D situations.

3.7.5.3 Magnetic flux and flux linkage (A-level only)

Content	Opportunities for skills development
Magnetic flux defined by $Φ = B A$ where $B$ is normal to $A$ . Flux linkage as $N Φ$ where $N$ is the number of turns cutting the flux. Flux and flux linkage passing through a rectangular coil rotated in a magnetic field: flux linkage $N Φ = B A N \cos θ$
Required practical 11: Investigate, using a search coil and oscilloscope, the effect on magnetic flux linkage of varying the angle between a search coil and magnetic field direction.

Content

Opportunities for skills development

Magnetic flux defined by $Φ = B A$ where $B$ is normal to $A$ .

Flux linkage as $N Φ$ where $N$ is the number of turns cutting the flux.

Flux and flux linkage passing through a rectangular coil rotated in a magnetic field:

flux linkage $N Φ = B A N \cos θ$

Required practical 11: Investigate, using a search coil and oscilloscope, the effect on magnetic flux linkage of varying the angle between a search coil and magnetic field direction.

3.7.5.4 Electromagnetic induction (A-level only)

Content	Opportunities for skills development
Simple experimental phenomena. Faraday’s and Lenz’s laws. Magnitude of induced emf = rate of change of flux linkage $ε = N \frac{∆ Φ}{∆ t}$ Applications such as a straight conductor moving in a magnetic field. emf induced in a coil rotating uniformly in a magnetic field: $ε = B A N ω \sin ω t$

Content

Opportunities for skills development

Simple experimental phenomena.

Faraday’s and Lenz’s laws.

Magnitude of induced emf = rate of change of flux linkage $ε = N \frac{∆ Φ}{∆ t}$

Applications such as a straight conductor moving in a magnetic field.

emf induced in a coil rotating uniformly in a magnetic field: $ε = B A N ω \sin ω t$

3.7.5.5 Alternating currents (A-level only)

Content	Opportunities for skills development
Sinusoidal voltages and currents only; root mean square, peak and peak-to-peak values for sinusoidal waveforms only. $I_{rms} = \frac{I_{0}}{\sqrt{2}}$ $; V_{rms} = \frac{V_{0}}{\sqrt{2}}$ Application to the calculation of mains electricity peak and peak-to-peak voltage values. Use of an oscilloscope as a dc and ac voltmeter, to measure time intervals and frequencies, and to display ac waveforms. No details of the structure of the instrument are required but familiarity with the operation of the controls is expected.

Content

Opportunities for skills development

Sinusoidal voltages and currents only; root mean square, peak and peak-to-peak values for sinusoidal waveforms only.

$I_{rms} = \frac{I_{0}}{\sqrt{2}}$ $; V_{rms} = \frac{V_{0}}{\sqrt{2}}$

Application to the calculation of mains electricity peak and peak-to-peak voltage values.

Use of an oscilloscope as a dc and ac voltmeter, to measure time intervals and frequencies, and to display ac waveforms.

No details of the structure of the instrument are required but familiarity with the operation of the controls is expected.

3.7.5.6 The operation of a transformer (A-level only)

Content	Opportunities for skills development
The transformer equation: $\frac{N_{s}}{N_{p}} = \frac{V_{s}}{V_{p}}$ Transformer efficiency = $\frac{I_{S} V_{S}}{I_{P} V_{P}}$ Production of eddy currents. Causes of inefficiencies in a transformer. Transmission of electrical power at high voltage including calculations of power loss in transmission lines.	MS 0.3 / AT b, h Investigate relationships between currents, voltages and numbers of coils in transformers.

Content

Opportunities for skills development

The transformer equation: $\frac{N_{s}}{N_{p}} = \frac{V_{s}}{V_{p}}$

Transformer efficiency = $\frac{I_{S} V_{S}}{I_{P} V_{P}}$

Production of eddy currents.

Causes of inefficiencies in a transformer.

Transmission of electrical power at high voltage including calculations of power loss in transmission lines.

MS 0.3 / AT b, h

Investigate relationships between currents, voltages and numbers of coils in transformers.

3.6 Further mechanics and thermal physics (A-level only)

3.8 Nuclear physics (A-level only)

Content	Opportunities for skills development
Concept of a force field as a region in which a body experiences a non-contact force. Students should recognise that a force field can be represented as a vector, the direction of which must be determined by inspection. Force fields arise from the interaction of mass, of static charge, and between moving charges. Similarities and differences between gravitational and electrostatic forces: Similarities: Both have inverse-square force laws that have many characteristics in common, eg use of field lines, use of potential concept, equipotential surfaces etc Differences: masses always attract, but charges may attract or repel

Content	Opportunities for skills development
Gravity as a universal attractive force acting between all matter. Magnitude of force between point masses: $F = \frac{G m_{1} m_{2}}{r^{2}}$ where $G$ is the gravitational constant.	MS 0.4 Students can estimate the gravitational force between a variety of objects.

Content

Opportunities for skills development

Gravity as a universal attractive force acting between all matter.

Magnitude of force between point masses: $F = \frac{G m_{1} m_{2}}{r^{2}}$ where $G$ is the gravitational constant.

MS 0.4

Students can estimate the gravitational force between a variety of objects.

Content	Opportunities for skills development
Representation of a gravitational field by gravitational field lines. $g$ as force per unit mass as defined by $g = \frac{F}{m}$ Magnitude of $g$ in a radial field given by $g = \frac{G M}{r^{2}}$

Content

Opportunities for skills development

Representation of a gravitational field by gravitational field lines.

$g$ as force per unit mass as defined by $g = \frac{F}{m}$

Magnitude of $g$ in a radial field given by $g = \frac{G M}{r^{2}}$

Content	Opportunities for skills development
Understanding of definition of gravitational potential, including zero value at infinity. Understanding of gravitational potential difference. Work done in moving mass $m$ given by $∆ W = m ∆ V$ Equipotential surfaces. Idea that no work is done when moving along an equipotential surface. $V$ in a radial field given by $V = - \frac{G M}{r}$ Significance of the negative sign. Graphical representations of variations of $g$ and $V$ with $r$ . $V$ related to $g$ by: $g = - \frac{∆ V}{∆ r}$ $∆ V$ from area under graph of $g$ against $r$ .	MS 3.8, 3.9 Students use graphical representations to investigate relationships between $v$ , $r$ and $g$ .

Content

Opportunities for skills development

Understanding of definition of gravitational potential, including zero value at infinity.

Understanding of gravitational potential difference.

Work done in moving mass $m$ given by $∆ W = m ∆ V$

Equipotential surfaces.

Idea that no work is done when moving along an equipotential surface.

$V$ in a radial field given by $V = - \frac{G M}{r}$

Significance of the negative sign.

Graphical representations of variations of $g$ and $V$ with $r$ .

$V$ related to $g$ by: $g = - \frac{∆ V}{∆ r}$

$∆ V$ from area under graph of $g$ against $r$ .

MS 3.8, 3.9

Students use graphical representations to investigate relationships between $v$ , $r$ and $g$ .

Content	Opportunities for skills development
Orbital period and speed related to radius of circular orbit; derivation of $T^{2} \propto r^{3}$ Energy considerations for an orbiting satellite. Total energy of an orbiting satellite. Escape velocity. Synchronous orbits. Use of satellites in low orbits and geostationary orbits, to include plane and radius of geostationary orbit.	MS 0.4 Estimate various parameters of planetary orbits, eg kinetic energy of a planet in orbit. MS 3.11 Use logarithmic plots to show relationships between $T$ and $r$ for given data.

Content

Opportunities for skills development

Orbital period and speed related to radius of circular orbit; derivation of $T^{2} \propto r^{3}$

Energy considerations for an orbiting satellite.

Total energy of an orbiting satellite.

Escape velocity.

Synchronous orbits.

Use of satellites in low orbits and geostationary orbits, to include plane and radius of geostationary orbit.

MS 0.4

Estimate various parameters of planetary orbits, eg kinetic energy of a planet in orbit.

MS 3.11

Use logarithmic plots to show relationships between $T$ and $r$ for given data.

Content	Opportunities for skills development
Force between point charges in a vacuum: $F = \frac{1}{4 π ε_{0}} \frac{Q_{1} Q_{2}}{r^{2}}$ Permittivity of free space, $ε_{0}$ Appreciation that air can be treated as a vacuum when calculating force between charges. For a charged sphere, charge may be considered to be at the centre. Comparison of magnitude of gravitational and electrostatic forces between subatomic particles.	MS 0.3, 2.3 Students can estimate the magnitude of the electrostatic force between various charge configurations.

Content

Opportunities for skills development

Force between point charges in a vacuum:

$F = \frac{1}{4 π ε_{0}} \frac{Q_{1} Q_{2}}{r^{2}}$

Permittivity of free space, $ε_{0}$

Appreciation that air can be treated as a vacuum when calculating force between charges.

For a charged sphere, charge may be considered to be at the centre.

Comparison of magnitude of gravitational and electrostatic forces between subatomic particles.

MS 0.3, 2.3

Students can estimate the magnitude of the electrostatic force between various charge configurations.

Content	Opportunities for skills development
Representation of electric fields by electric field lines. Electric field strength. $E$ as force per unit charge defined by $E = \frac{F}{Q}$ Magnitude of $E$ in a uniform field given by $E = \frac{V}{d}$ Derivation from work done moving charge between plates: $F d = Q Δ V$ Trajectory of moving charged particle entering a uniform electric field initially at right angles. Magnitude of $E$ in a radial field given by $E = \frac{1}{4 π ε_{0}} \frac{Q}{r^{2}}$	PS 1.2, 2.2 / AT b Students can investigate the patterns of various field configurations using conducting paper (2D) or electrolytic tank (3D).

Content

Opportunities for skills development

Representation of electric fields by electric field lines.

Electric field strength.

$E$ as force per unit charge defined by $E = \frac{F}{Q}$

Magnitude of $E$ in a uniform field given by $E = \frac{V}{d}$

Derivation from work done moving charge between plates: $F d = Q Δ V$

Trajectory of moving charged particle entering a uniform electric field initially at right angles.

Magnitude of $E$ in a radial field given by $E = \frac{1}{4 π ε_{0}} \frac{Q}{r^{2}}$

PS 1.2, 2.2 / AT b

Students can investigate the patterns of various field configurations using conducting paper (2D) or electrolytic tank (3D).

Content	Opportunities for skills development
Understanding of definition of absolute electric potential, including zero value at infinity, and of electric potential difference. Work done in moving charge $Q$ given by $∆ W = Q ∆ V$ Equipotential surfaces. No work done moving charge along an equipotential surface. Magnitude of $V$ in a radial field given by $V = \frac{1}{4 π ε_{0}} \frac{Q}{r}$ Graphical representations of variations of $E$ and $V$ with $r$ . $V$ related to $E$ by $E = \frac{∆ V}{∆ r}$ $∆ V$ from the area under graph of $E$ against $r$ .

Content

Opportunities for skills development

Understanding of definition of absolute electric potential, including zero value at infinity, and of electric potential difference.

Work done in moving charge $Q$ given by $∆ W = Q ∆ V$

Equipotential surfaces.

No work done moving charge along an equipotential surface.

Magnitude of $V$ in a radial field given by $V = \frac{1}{4 π ε_{0}} \frac{Q}{r}$

Graphical representations of variations of $E$ and $V$ with $r$ .

$V$ related to $E$ by $E = \frac{∆ V}{∆ r}$

$∆ V$ from the area under graph of $E$ against $r$ .

Content

Opportunities for skills development

Definition of capacitance: $C = \frac{Q}{V}$

Content	Opportunities for skills development
Dielectric action in a capacitor $C = \frac{A ε_{0} ε_{r}}{d}$ Relative permittivity and dielectric constant. Students should be able to describe the action of a simple polar molecule that rotates in the presence of an electric field.	PS 1.2, 2.2, 4.3 / AT f, g Determine the relative permittivity of a dielectric using a parallel-plate capacitor. Investigate the relationship between $C$ and the dimensions of a parallel-plate capacitor eg using a capacitance meter.

Content

Opportunities for skills development

Dielectric action in a capacitor $C = \frac{A ε_{0} ε_{r}}{d}$

Relative permittivity and dielectric constant.

Students should be able to describe the action of a simple polar molecule that rotates in the presence of an electric field.

PS 1.2, 2.2, 4.3 / AT f, g

Determine the relative permittivity of a dielectric using a parallel-plate capacitor.

Investigate the relationship between $C$ and the dimensions of a parallel-plate capacitor eg using a capacitance meter.

Content	Opportunities for skills development
Interpretation of the area under a graph of charge against pd. $E = \frac{1}{2} Q V = \frac{1}{2} C V^{2} = \frac{1}{2} \frac{Q^{2}}{C}$

Content

Opportunities for skills development

Interpretation of the area under a graph of charge against pd.

$E = \frac{1}{2} Q V = \frac{1}{2} C V^{2} = \frac{1}{2} \frac{Q^{2}}{C}$

Content	Opportunities for skills development
Graphical representation of charging and discharging of capacitors through resistors. Corresponding graphs for $Q$ , $V$ and $I$ against time for charging and discharging. Interpretation of gradients and areas under graphs where appropriate. Time constant $R C$ . Calculation of time constants including their determination from graphical data. Time to halve, $T_{½} = 0.69 R C$ Quantitative treatment of capacitor discharge, $Q = Q_{0} e^{- \frac{t}{R C}}$ Use of the corresponding equations for $V$ and $I$ . Quantitative treatment of capacitor charge, $Q = Q_{0} (1 - e^{- \frac{t}{R C}})$
Required practical 9: Investigation of the charge and discharge of capacitors. Analysis techniques should include log-linear plotting leading to a determination of the time constant, $R C$	MS 3.8, 3.10, 3.11 / PS 2.2, 2.3 / AT f, k

Content

Opportunities for skills development

Graphical representation of charging and discharging of capacitors through resistors. Corresponding graphs for $Q$ , $V$ and $I$ against time for charging and discharging.

Interpretation of gradients and areas under graphs where appropriate.

Time constant $R C$ .

Calculation of time constants including their determination from graphical data.

Time to halve, $T_{½} = 0.69 R C$

Quantitative treatment of capacitor discharge, $Q = Q_{0} e^{- \frac{t}{R C}}$

Use of the corresponding equations for $V$ and $I$ .

Quantitative treatment of capacitor charge, $Q = Q_{0} (1 - e^{- \frac{t}{R C}})$

Required practical 9: Investigation of the charge and discharge of capacitors. Analysis techniques should include log-linear plotting leading to a determination of the time constant, $R C$

MS 3.8, 3.10, 3.11 / PS 2.2, 2.3 / AT f, k

Content	Opportunities for skills development
Force on a current-carrying wire in a magnetic field: $F = B I l$ when field is perpendicular to current. Fleming’s left hand rule. Magnetic flux density $B$ and definition of the tesla.
Required practical 10: Investigate how the force on a wire varies with flux density, current and length of wire using a top pan balance.

Content

Opportunities for skills development

Force on a current-carrying wire in a magnetic field: $F = B I l$ when field is perpendicular to current.

Fleming’s left hand rule.

Magnetic flux density $B$ and definition of the tesla.

Required practical 10: Investigate how the force on a wire varies with flux density, current and length of wire using a top pan balance.

Content	Opportunities for skills development
Force on charged particles moving in a magnetic field, $F = B Q v$ when the field is perpendicular to velocity. Direction of force on positive and negative charged particles. Circular path of particles; application in devices such as the cyclotron.	MS 4.3 Convert between 2D representations and 3D situations.

Content

Opportunities for skills development

Force on charged particles moving in a magnetic field, $F = B Q v$ when the field is perpendicular to velocity.

Direction of force on positive and negative charged particles.

Circular path of particles; application in devices such as the cyclotron.

MS 4.3

Convert between 2D representations and 3D situations.

Content	Opportunities for skills development
Magnetic flux defined by $Φ = B A$ where $B$ is normal to $A$ . Flux linkage as $N Φ$ where $N$ is the number of turns cutting the flux. Flux and flux linkage passing through a rectangular coil rotated in a magnetic field: flux linkage $N Φ = B A N \cos θ$
Required practical 11: Investigate, using a search coil and oscilloscope, the effect on magnetic flux linkage of varying the angle between a search coil and magnetic field direction.

Content

Opportunities for skills development

Magnetic flux defined by $Φ = B A$ where $B$ is normal to $A$ .

Flux linkage as $N Φ$ where $N$ is the number of turns cutting the flux.

Flux and flux linkage passing through a rectangular coil rotated in a magnetic field:

flux linkage $N Φ = B A N \cos θ$

Required practical 11: Investigate, using a search coil and oscilloscope, the effect on magnetic flux linkage of varying the angle between a search coil and magnetic field direction.

Content	Opportunities for skills development
Simple experimental phenomena. Faraday’s and Lenz’s laws. Magnitude of induced emf = rate of change of flux linkage $ε = N \frac{∆ Φ}{∆ t}$ Applications such as a straight conductor moving in a magnetic field. emf induced in a coil rotating uniformly in a magnetic field: $ε = B A N ω \sin ω t$

Content

Opportunities for skills development

Simple experimental phenomena.

Faraday’s and Lenz’s laws.

Magnitude of induced emf = rate of change of flux linkage $ε = N \frac{∆ Φ}{∆ t}$

Applications such as a straight conductor moving in a magnetic field.

emf induced in a coil rotating uniformly in a magnetic field: $ε = B A N ω \sin ω t$

Content	Opportunities for skills development
Sinusoidal voltages and currents only; root mean square, peak and peak-to-peak values for sinusoidal waveforms only. $I_{rms} = \frac{I_{0}}{\sqrt{2}}$ $; V_{rms} = \frac{V_{0}}{\sqrt{2}}$ Application to the calculation of mains electricity peak and peak-to-peak voltage values. Use of an oscilloscope as a dc and ac voltmeter, to measure time intervals and frequencies, and to display ac waveforms. No details of the structure of the instrument are required but familiarity with the operation of the controls is expected.

Content

Opportunities for skills development

Sinusoidal voltages and currents only; root mean square, peak and peak-to-peak values for sinusoidal waveforms only.

$I_{rms} = \frac{I_{0}}{\sqrt{2}}$ $; V_{rms} = \frac{V_{0}}{\sqrt{2}}$

Application to the calculation of mains electricity peak and peak-to-peak voltage values.

Use of an oscilloscope as a dc and ac voltmeter, to measure time intervals and frequencies, and to display ac waveforms.

No details of the structure of the instrument are required but familiarity with the operation of the controls is expected.

Content	Opportunities for skills development
The transformer equation: $\frac{N_{s}}{N_{p}} = \frac{V_{s}}{V_{p}}$ Transformer efficiency = $\frac{I_{S} V_{S}}{I_{P} V_{P}}$ Production of eddy currents. Causes of inefficiencies in a transformer. Transmission of electrical power at high voltage including calculations of power loss in transmission lines.	MS 0.3 / AT b, h Investigate relationships between currents, voltages and numbers of coils in transformers.

Content

Opportunities for skills development

The transformer equation: $\frac{N_{s}}{N_{p}} = \frac{V_{s}}{V_{p}}$

Transformer efficiency = $\frac{I_{S} V_{S}}{I_{P} V_{P}}$

Production of eddy currents.

Causes of inefficiencies in a transformer.

Transmission of electrical power at high voltage including calculations of power loss in transmission lines.

MS 0.3 / AT b, h

Investigate relationships between currents, voltages and numbers of coils in transformers.