Fields: gravitational & electric

1. Fields: gravitational & electric

2. Learning outcomes • describe uniform and radial electric and gravitational fields in terms of force, field strength and potential, using equations, graphs and the conventional line diagrams • describe similarities and differences between electric and gravitational fields • solve quantitative problems involving gravitational and electric fields, including orbits

3. Teaching challenges Helping students to understand several ways of describing fields (pictures, graphs, equations) and developing their ability to ‘translate’ between each of them.

4. Forces quantitatively Newton’s law of universal gravitation (1687) G = 6.67 x 10-11 N m2 kg-2 Coulomb’s law (1783) in vacuum, k = 9.0 x 109 N m2 C-2

5. Permittivity The strength of the electric field will also depend upon what material is between the two charges. This is known as the permittivity, ε. The permittivity of air is taken to be that of a vacuum, and is called the permittivity of free space, εo. εo =8.85 x 10-12UNIT?

6. Superposition of electric forces Find the magnitude and direction of the resultant force on the red charge. Charge spacing is 1m.

7. Kepler’s laws describe planetary motion (1605, obtained empirically) 1 The orbit of every planet is an ellipse with the Sun at one focus. 2 The line joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3 A planet’s distance from the Sun, R, and its orbital period, T, are related.

8. Newton explains orbits The centripetal force is supplied by gravity. Kepler 3:

9. Practice questions 1 • TAP Newton’s law of universal gravitation

10. Gravitational fields used to explain (in some cases, control) • everyday situations involving lifting & falling, floating & sinking, including transport (ship, road, rail, hot air balloons, aviation) • some machines in children’s playgrounds, adventure park rides • variation of g with latitude, altitude, anomalies associated with mineral deposits, plate tectonics • solar system mechanics – moons, planets, meteors, asteroids • star formation, galaxies, Universe • space launches, mission paths and orbits

11. Electric fields used to explain (in some cases, control) • natural phenomena such as thunderstorms, solar wind • static electricity & antistatic devices & procedures • electric circuits of many kinds • computer processors and memory • atomic structure, electrolysis • industrial processes such as spray painting • devices such as spark plugs and photocopiers • particle accelerators

12. Field line representation First drawn by Michael Faraday (~1820) • direction of forceacting on a small test object at different locations • magnitude of force: where field lines are … close together = strong field far apart = weak field parallel and equally spaced = uniform field • field lines cannot cross Fields are often 3-dimensional. Field concept: forces act locally (field ‘fills space’), not action ‘at a distance’.

13. Possible shapes for fields uniform (e.g. capacitor) cylindrical (e.g. coaxial cable) radial (e.g Van de Graaff dome)

14. Similarities and differences gravitational field strength, unit: N kg-1 force attractive only electric field strength, unit: N C-1 or V m-1 force can be attractive or repulsive. Small test charge +q Note: field strength is a property of the field at a point, and is independent of the object placed there.

15. Uniform field Lines of force are parallel. Force on a ‘test’ charge is same, whatever its position. PP experiment Electric fields (using grass seed) Projectile motion • in a uniform gravitational field • in a uniform electric field PP experiment Electron deflection tube: using an electric field

16. The oscilloscope

17. Producing an electron beam PP experiment The "electron gun" or valve diode • heater (hot filament) • thermionic emission of electrons • accelerating field • shaped anode (hole)

18. Calculating electron speed The field doeswork W on the electron Example: V = 5 kV. e = 1.6 x 10-19 C m = 9.1 x 10-31 kg Show that electron v = 4.2 x 107 ms-1 [ignoring relativistic effects]

19. A linear accelerator The polarity of each section is periodically reversed, so that electrons are repeatedly accelerated across the gaps. Note that tube lengths increase as electrons travel faster.

20. Gravitational EP Close to the Earth, we can assume that the change in gravitational field strength with height is negligible. The gravitational field is uniform. Lift a mass, m. Potential energy gained,EP= work done = force of gravitational field on mass x lift height EP= mg ∆h

21. Field potential gravitational field field potential = potential energyper unit mass unit: J kg-1 electric field field potential = potential energyper unit charge unit: J C-1 Like field strength, potential is a property of the field at a point and is independent of the object placed there.

22. Potential difference change in potential between points A and B.

23. Representing field potential equipotential lines Work can be done on the field (increasing potential) or by the field (decreasing potential). force lines and equipotential lines are perpendicular An object can move along an equipotential line without changing its potential energy.

24. Describing fields: summary

25. Practice questions 2 (Adv Phys) Gravitational potential energy and gravitational potential Practice in Physics Qs 20.24 – 20.30

26. Potential gradient An electron is accelerated across a uniform electric field. Work done by the field, Minus sign: The energy of the electron falls as it moves in the direction of the force. In general: field strength = - potential gradient

27. Sparks and ionisation What is the p.d. across the terminals of a spark plug? [Assume the field strength required to ionise the mixture is 6 x 106 V m-1 and the field is uniform.]

28. The Earth’s field is spherical The spacing of equipotential lines falls with distance.

29. Radial field of a point charge or mass NOTE: F and Ep are 0 at infinity • field around a mass or negative charge is attractive. This means that F, Ep get increasingly negative with smaller r. • field around a positive charge is repulsive. This means that F, Ep get increasingly positive with smaller r.

30. Force in a radial field Inverse square law Double the distance and the force reduces to a quarter.

31. Ep in a radial field Force decreases with the square of the distance from the positively charged sphere. Move an object a small distance δr Force = Total work done = area under the whole curve.

32. Practice questions 3 Practice in Physics Qs 20.36, 39, 40, 43, 44 Electric field simulations Falstad Caltech PhET