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# 10.1 describing fields 2015

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### 10.1 describing fields 2015

1. 1. Topic 10 Topic 10.1 Describing fields
2. 2. When forces act at a distance, physicists use the notion of a field to explain this. How can you describe a field? What produces fields?
3. 3. GRAVITATIONAL FIELDS
4. 4. Gravitational Field Strength A mass M creates a gravitational field in space around it. If a mass m is placed at some point in space around the mass M it will experience the existance of the field in the form of a gravitational force Recap
5. 5. We define the gravitational field strength as the ratio of the force the mass m would experience to the mass, m That is the gravitational field strength at a point, it is the force exerted per unit mass on a particle of small mass placed at that point Recap
6. 6. The force experienced by a mass m placed a distance r from a mass M is F = G Mm r2 And so the gravitational field strength of the mass M is g = G M r2 Recap
7. 7. The units of gravitational field strength are N kg-1 The gravitational field strength is a vector quantity whose direction is given by the direction of the force a mass would experience if placed at the point of interest Recap
8. 8. Field Strength at the Surface of a Planet If we replace the particle M with a sphere of mass M and radius R then relying on the fact that the sphere behaves as a point mass situated at its centre the field strength at the surface of the sphere will be given by g = G M R2 Recap
9. 9. If the sphere is the Earth then we have g = G Me Re 2 But the field strength is equal to the acceleration that is produced on the mass, hence we have that the acceleration of free fall at the surface of the Earth, g g = G Me Re 2 Recap
10. 10. Gravitational Energy and Potential We know that the gravitational potential energy increases as a mass is raised above the Earth The work done in moving a mass between two points is positive when moving away from the Earth By definition the gravitational potential energy is taken as being zero at infinity It is a scalar quantity
11. 11. The gravitational potential at any point in the Earth´s field is given by the formula V = - G Me r Where r is the distance from the centre of the Earth (providing r >R) The negative sign allows for the fact that all the potentials are negative as they have to increase to zero
12. 12. Definition The potential is therefore a measure of the amount of work that has to be done to move particles between points in a gravitational field and its units are J kg –1 The work done is independent of the path taken between the two points in the field, as it is the difference between the initial and final potentials that give the value
13. 13. Graphs Gravitational field strength versus distance g α 1/r2 Gravitational potential versus distance V α -1/r
14. 14. ELECTROSTATIC FIELDS
15. 15. If a very small, positive point charge Q, the test charge, is placed at any point in an electric field and it experiences a force F, then the field strength E (also called the E-field) at that point is defined by the equation 𝐸 = 𝐹 𝑞 Recap
16. 16. The magnitude of E is the force per unit charge and its direction is that of F (i.e. of the force which acts on a positive charge). If F is in newtons (N) and Q is in coulombs (C) then the unit of E is the newton per coulomb (N C-1). Recap
17. 17. Coulomb’s Law Coulomb’s law states that the force acting between two charges q1 and q2 whose distances are separated by a distance d is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The force is along the line joining the centres of the charges. Recap
18. 18. Coulomb’s Law 𝑭 = 𝟏 𝟒𝝅𝜺𝜺 𝒐 𝒒 𝟏 𝒒 𝟐 𝒓 𝟐 Recap
19. 19. Electric Potential due to a Point Charge The electric potential at a point in an electric field is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to the point. Electric potential is a scalar quantity and it has the volt V as its unit. Based on this definition, the potential at infinity is zero.
20. 20. Let us take a point r metres from a charged object. The potential at this point can be calculated using the following
21. 21. Electric Field Strength and Potential Suppose that the charge +q is moved a small distance by a force F from A to B so that the force can be considered constant.
22. 22. The work done is given by: ΔW = Fx Δx The force F and the electric field E are oppositely directed, and we know that: F = -q x E Therefore, the work done can be given as: ΔW = -qE x Δ x = qV
23. 23. Therefore E = - ΔV / Δx This is the potential gradient.
24. 24. Electric Field and Potential due to a charged sphere
25. 25. When the sphere becomes charged, we know that the charge distributes itself evenly over the surface. Therefore every part of the material of the conductor is at the same potential. As the electric potential at a point is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to that point, it has a constant value in every part of the material of the conductor,
26. 26. Since the potential is the same at all points on the conducting surface, then Δ V / Δx is zero. But E = - Δ V / Δ x. Therefore, the electric field inside the conductor is zero. There is no electric field inside the conductor.
27. 27. Equipotentials Regions in space where the electric potential of a charge distribution has a constant value are called equipotentials. The places where the potential is constant in three dimensions are called equipotential surfaces, and where they are constant in two dimensions they are called equipotential lines.
28. 28. They are in some ways analogous to the contour lines on topographic maps. Similar also to gravitational potential. In this case, the gravitational potential energy is constant as a mass moves around the contour lines because the mass remains at the same elevation above the earth's surface. The gravitational field strength acts in a direction perpendicular to a contour line.
29. 29. Similarly, because the electric potential on an equipotential line has the same value, no work can be done by an electric force when a test charge moves on an equipotential. Therefore, the electric field cannot have a component along an equipotential, and thus it must be everywhere perpendicular to the equipotential surface or equipotential line. This fact makes it easy to plot equipotentials if the lines of force or lines of electric flux of an electric field are known.
30. 30. In this image the lines are equally spaced…it is a uniform field In the real world the lines are surfaces, but we cant show that on paper very well
31. 31. Equipotentials for 2 point masses is like two positive charges
32. 32. For example, there are a series of equipotential lines between two parallel plate conductors that are perpendicular to the electric field. There will be a series of concentric circles that map out the equipotentials around an isolated positive sphere. The lines of force and some equipotential lines for an isolated positive sphere are shown in the next figures.