Topic 6: Fields and forces

1. Topic 6: Fields and forces 6.1 Gravitational force and field Students should be aware that the masses in the force law are point masses. The force between two spherical masses whose separation is large compared to their radii is the same as if the two spheres were point masses with their masses concentrated at the centers of the spheres. State Newton’s universal law of gravitation.

2. Newton 1642-1727 F = Gm1m2 r2 Newton’s laws of gravitation Anything with mass attracts anything else with mass. The size of that attraction is given by my Law of Gravitation: State Newton’s universal law of gravitation. …where m1 and m2 are the masses of the two objects (in kg), r is the distance between them (in m) and G is “The Universal Gravitational Constant” (= 6.67 x 10-11 Nm2kg-2).

3. Cavendish measurement of G Click to play

5. Inverse square law

6. What holds the planet in orbit?

7. Free Body Force Diagrams revision The Earth attracts the man and the man attracts the Earth – a Newton III pair of forces where both are gravitational.

8. A uniform gravitational field is one where the field lines are always the same distance apart - this is almost exactly true close to the Earth's surface (Figure 1(a)). However if we move back and look at the planet from a distance the field lines clearly radiate outwards (Figure 1(b)), getting further apart as the distance from the Earth increases. When viewed from an even greater distance the complete field can be seen (Figure 1(c)). Such a field is called a radial field - the field intensity (g) decreasing with distance. Diagram 1(d) shows the distortion of the gravitational field lines by high- density rock.

9. GMm = mg r2 GM = g r2 Gravitational Field Strength Derive an expression for gravitational field strength at the surface of a planet, assuming that all its mass is concentrated at its centre. Consider a man on the Earth: Man’s weight = mg BUT we know that this is equal to his gravitational attraction, so… Therefore: (this is a vector quantity)

10. Gravitational Field Strength Define gravitational field strength. Definition: Force, act, point, unit mass. Write a definition of gravitational field strength Determine the gravitational field due to one or more point masses. Derive an expression for gravitational field strength at the surface of a planet, assuming that all its mass is concentrated at its centre.

11. 6.2 Electric force and field State that there are two types of electric charge.

12. - - + - - + + - - - - - Static Electricity

13. Conservation of charge State and apply the law of conservation of charge. The law of conservation of charge states……………. One of the fundamental laws of Physics is that charge can never be created or destroyed. Charge is always conserved in any reaction. A simple example of this is the rubbing of a polythene strip with a duster. Initially the strip and the dusted were uncharged but after rubbing the strip gains a net negative charge and the duster gains an equal amount of positive charge – the total charge in the process has been conserved.

14. Conductors and insulators. Describe and explain the difference in the electrical properties of conductors and insulators. The difference between conductors and insulators is……………… In a conductor, the conduction and valence bands overlap. This allows the valence electrons to easily move along the conduction band giving the material low electrical resistance. In insulators, there is a large forbidden energy band, which makes it difficult for valence electrons to move into the conduction band giving the material a high electrical resistance. In semiconductors, the forbidden energy band is not too wide. Under certain conditions, electrons in the valence band can gain sufficient energy to cross the gap. This reduces the electrical resistance of the material.

15. Coulomb’s law Students should be aware that the charges in the force law are point charges. State Coulomb’s law.

16. F = kQ1Q2 r2 Coulomb’s Law Charles Coulomb 1736-1806 Coulomb’s Law Like gravity, electrostatic force is one of the four fundamental forces. The equation looks pretty similar too… …where k = 9.0 x 109 Nm2C-2 (the “Coulomb Law Constant”). This comes from k = 1/4πε0 … …where ε0 = permittivity of free space (i.e. 8.85 x 10-12 Fm-1).

17. Electric field of a point charge Define electric field strength. Write a definition of electric field strength Students should understand the concept of a test charge. Determine the electric field strength due to one or more point charges.

18. Electric field patterns Draw the electric field patterns for different charge configurations. These include the fields due to the following charge configurations: a point charge, a charged sphere, two point charges, and oppositely charged parallel plates. The latter includes the edge effect. Students should understand what is meant by radial field.

19. How do we predict the shape of a field? • Imagine that you have a unit positive test charge. • Place it in a point in the field. • Sketch the path it would take. • Repeat this many times until you have enough field lines • The “density” of the lines represents the strength of the field.

20. Point charge +

21. Sphere Positive or negative

22. 2 Point charges + +

23. 2 Point charges + -

24. Parallel plates + _ Edge effects

25. Electric field strength E = F q F = kQq r2 Coulomb’s Law Electric field strength E = kQ (in NC-1) r2 Electric Fields (this is a bit like gravitional field strength g = F/m) Let’s compare this to Coulomb’s Law: Putting these equations together gives us…

26. Using mv2 = kQq we get v = 1.5x106 ms-1 r r2 Electrostatic force and circular motion Consider an electron orbiting a nucleus in a hydrogen atom: e Q. If the mass of an electron is 9.1x10-31kg and the distance to the proton is 0.11nm how fast is the electron going? p

27. - - - - - - - - - A practical example Consider a charged polythene strip and a metal ball: - + + - - + + -

28. Fields applet

29. Field for a point charge Click to play

30. Electric dipole Click to play

31. Falstad.com Falstad.com

32. Electric fields around a point charge Draw the edge effects for the parallel plate http://www.falstad.com/emstatic/ 2 Charged Spheres

34. + V - Uniform electric fields Consider two charged plates: Now consider a point charge: Work done = QV Q For an electron, eV = ½mv2

35. Visualising the fields Hyperlink

36. 6.3 Magnetic force and field

37. Permanent magnets and domains

38. State that moving charges give rise to magnetic fields. Hyperlink Draw magnetic field patterns due to currents. These include the fields due to currents in a straight wire, a flat circular coil and a solenoid.

39. Field around a wire Click to play

40. Field around a loop Click to play

41. B field for a loop Click to play

42. Field patterns

43. Left hand Motor Rule Determine the direction of the force on a current-carrying conductor in a magnetic field.

44. Fleming's left- hand rule

45. N S Current-carrying wire in a magnetic field F = Force B = Magnetic field I = Current Q. Where will this wire go?

46. N S Comparing magnets and solenoids Magnet: Solenoid:

47. Magnetic Field around a Solenoid

48. Forces on a loop Click to play

49. Electric motor Click to play

50. Hyperlink