A-level Physics₇₄₀₈

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

Gravity as a universal attractive force acting between all matter.

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

MS 0.4

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

Representation of a gravitational field by gravitational field lines.

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

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

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

Understanding of gravitational potential difference.

Work done in moving mass $\mathit{m}$ given by $\mathrm{∆}\mathit{W}\mathsf{=}\mathit{m}\mathrm{∆}\mathit{V}$

Equipotential surfaces.

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

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

Significance of the negative sign.

Graphical representations of variations of $\mathit{g}$ and $\mathit{V}$ with $\mathit{ }\mathit{r}$ .

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

$\mathsf{∆}\mathit{V}$ from area under graph of $\mathit{g}$ against $\mathit{r}$ .

MS 3.8, 3.9

Students use graphical representations to investigate relationships between $\mathit{v}$ , $\mathit{r}$ and $\mathit{g}$ .

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

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 $\mathit{T}$ and $\mathit{r}$ for given data.

Force between point charges in a vacuum:

$\mathit{F}\mathsf{=}\frac{\mathsf{1}}{\mathsf{4}\mathit{\pi }{\mathit{\epsilon }}_{\mathsf{0}}}\frac{{\mathit{Q}}_{\mathsf{1}}{\mathit{Q}}_{\mathsf{2}}}{{\mathit{r}}^{\mathsf{2}}}$

Permittivity of free space, ${\mathit{\epsilon }}_{\mathsf{0}}$

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.

Representation of electric fields by electric field lines.

Electric field strength.

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

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

Derivation from work done moving charge between plates: $\mathit{F}\mathit{d}\mathsf{=}\mathit{ }\mathit{Q}\mathrm{\Delta }\mathit{V}$

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

Magnitude of $\mathit{E}$ in a radial field given by $\mathit{E}\mathsf{=}\frac{\mathsf{1}}{\mathsf{4}\mathit{\pi }{\mathit{\epsilon }}_{\mathsf{0}}}\frac{\mathit{Q}}{{\mathit{r}}^{\mathsf{2}}}$

PS 1.2, 2.2 / AT b

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

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

Work done in moving charge $\mathit{Q}$ given by $\mathsf{∆}\mathit{W}\mathsf{=}\mathit{Q}\mathsf{∆}\mathit{V}$

Equipotential surfaces.

No work done moving charge along an equipotential surface.

Magnitude of $\mathit{V}$ in a radial field given by $\mathit{V}\mathsf{=}\frac{\mathsf{1}}{\mathsf{4}\mathit{\pi }{\mathit{\epsilon }}_{\mathsf{0}}}\frac{\mathit{Q}}{\mathit{r}}$

Graphical representations of variations of $\mathit{E}$ and $\mathit{V}$ with $\mathit{r}$ .

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

$\mathrm{∆}\mathit{V}$ from the area under graph of $\mathit{E}\mathit{ }$ against $\mathit{r}$ .

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

Dielectric action in a capacitor $\mathit{C}\mathsf{=}\frac{\mathit{A}{\mathit{\epsilon }}_{\mathsf{0}}{\mathit{\epsilon }}_{\mathsf{r}}}{\mathit{d}}$

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 $\mathit{C}$ and the dimensions of a parallel-plate capacitor eg using a capacitance meter.

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

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

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

Interpretation of gradients and areas under graphs where appropriate.

Time constant $\mathit{R}\mathit{C}$ .

Calculation of time constants including their determination from graphical data.

Time to halve, ${\mathit{T}}_{\mathrm{½}}\mathsf{=}\mathsf{0.69}\mathit{R}\mathit{C}$

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

Use of the corresponding equations for $\mathit{V}$ and $\mathit{I}$ .

Quantitative treatment of capacitor charge, $\mathit{ }\mathit{Q}\mathsf{=}{\mathit{Q}}_{\mathrm{0}}\left(\mathsf{1}\mathsf{-}{\mathrm{e}}^{\mathsf{-}\frac{\mathit{t}}{\mathit{R}\mathit{C}}}\right)$

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, $\mathit{R}\mathit{C}$

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

Fleming’s left hand rule.

Magnetic flux density $\mathrm{B}$ and definition of the tesla.

Force on charged particles moving in a magnetic field, $\mathit{F}\mathsf{=}\mathit{B}\mathit{Q}\mathit{v}$ 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.

Magnetic flux defined by $\mathit{\Phi }\mathsf{=}\mathit{B}\mathit{A}$ where $\mathit{B}$ is normal to $\mathit{A}$ .

Flux linkage as $\mathit{N}\mathit{\Phi }$ where $\mathit{N}$ is the number of turns cutting the flux.

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

flux linkage $\mathit{N}\mathit{\Phi }\mathsf{=}\mathit{B}\mathit{A}\mathit{N}\cos \mathit{\theta }$

Simple experimental phenomena.

Faraday’s and Lenz’s laws.

Magnitude of induced emf = rate of change of flux linkage $\mathit{\epsilon }\mathsf{=}\mathit{N}\frac{\mathsf{∆}\mathit{\Phi }}{\mathsf{∆}\mathit{t}}$

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

emf induced in a coil rotating uniformly in a magnetic field: $\mathit{\epsilon }\mathsf{=}\mathit{B}\mathit{A}\mathit{N}\mathit{\omega }\mathit{sin}\mathit{ }\mathit{\omega }\mathit{t}$

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

${\mathit{I}}_{\mathrm{rms}}\mathsf{=}\frac{{\mathit{I}}_{\mathsf{0}}}{\sqrt{\mathsf{2}}}$ $\mathsf{;}\mathit{ }{\mathit{V}}_{\mathrm{rms}}\mathsf{=}\frac{{\mathit{V}}_{\mathsf{0}}}{\sqrt{\mathsf{2}}}$

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.

The transformer equation: $\mathit{ }\frac{{\mathit{N}}_{\mathrm{s}}}{{\mathit{N}}_{\mathrm{p}}}\mathsf{=}\frac{{\mathit{V}}_{\mathrm{s}}}{{\mathit{V}}_{\mathrm{p}}}$

Transformer efficiency = $\mathit{ }\frac{{\mathit{I}}_{\mathrm{S}}{\mathit{V}}_{\mathrm{S}}}{{\mathit{I}}_{\mathrm{P}}{\mathit{V}}_{\mathrm{P}}}$

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.