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# Electric Charges, Forces and Fields

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Physic II
Lecture 2

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### Electric Charges, Forces and Fields

1. 1. Electric Charges, Forces, and Fields
2. 2. Electric Charges Electric charge is a basic property of matter Two basic charges Positive and Negative Each having an absolute value of 1.6 x 10-19 Coulombs Experiments have shown that Like signed charges repel each other Unlike signed charges attract each other For an isolated system, the net charge of the system remains constant Charge Conservation
3. 3. Two basics type of materials Conductors Materials, such as metals, that allow the free movement of charges Insulators Materials, such as rubber and glass, that don’t allow the free movement of charges
4. 4. Coulomb’s Law Coulomb found that the electric force between two charged objects is Proportional to the product of the charges on the objects, and Inversely proportional to the separation of the objects squared 2 21 r qq kF k being a proportionality constant, having a value of 8.988 x 109 Nm2/c2
5. 5. Electric Force 122 21 12 ˆr r qq kF  This gives the force on charged object 2 due to charged object 1 The direction of the force is either parallel or antiparallel to this unit vector depending upon the relative signs of the charges 12ˆr is a unit vector pointing from object 1 to object 2 As with all forces, the electric force is a Vector So we rewrite Coulomb’s Law as q2q1
6. 6. Electric Force The force acting on each charged object has the same magnitude - but acting in opposite directions (Newton’s Third Law)2112 FF 
7. 7. More Than Two Charges q q1 q2 qqF 1  qqF 2  netF  If q1 were the only other charge, we would know the force on q due to q1 - qqF 1  If q2 were the only other charge, we would know the force on q due to q2 - qqF 2  Given charges q, q1, and q2 What is the net force if both charges are present? The net force is given by the Superposition Principle 21 FFFnet 
8. 8. Superposition of Forces If there are more than two charged objects interacting with each other The net force on any one of the charged objects is The vector sum of the individual Coulomb forces on that charged object ji r r q kqF ij ij i jj ˆ2 
9. 9. Note on constants k is in reality defined in terms of a more fundamental constant, known as the permittivity of free space. 2 2 12 0 0 C 10854.8 4 1 Nm xwith k
10. 10. Electric Field The Electric Force is like the Gravitational Force Action at a Distance The electric force can be thought of as being mediated by an electric field.
11. 11. What is a Field? A Field is something that can be defined anywhere in space A field represents some physical quantity (e.g., temperature, wind speed, force) It can be a scalar field (e.g., Temperature field) It can be a vector field (e.g., Electric field) It can be a “tensor” field (e.g., Space-time curvature)
12. 12. 77 82 83 68 55 66 83 75 80 90 91 75 71 80 72 84 73 82 88 92 77 88 88 73 64 A Scalar Field A scalar field is a map of a quantity that has only a magnitude, such as temperature
13. 13. 77 82 83 68 55 66 83 75 80 90 91 75 71 80 72 84 73 57 88 92 77 56 88 7364 A Vector Field A vector field is a map of a quantity that is a vector, a quantity having both magnitude and direction, such as wind
14. 14. Electric Field We say that when a charged object is put at a point in space, The charged object sets up an Electric Field throughout the space surrounding the charged object It is this field that then exerts a force on another charged object
15. 15. Electric Field Like the electric force, the electric field is also a vector If there is an electric force acting on an object having a charge qo, then the electric field at that point is given by 0q F E   (with the sign of q0 included)
16. 16. Electric Field The force on a positively charged object is in the same direction as the electric field at that point, While the force on a negative test charge is in the opposite direction as the electric field at the point
17. 17. Electric Field A positive charge sets up an electric field pointing away from the charge A negative charge sets up an electric field pointing towards the charge
18. 18. Electric Field r r q kE ˆ2  The electric field of a point charge can then be shown to be given by ji r r q k ij ij i jj qF ˆ2 Earlier we saw that the force on a charged object is given by The term in parentheses remains the same if we change the charge on the object at the point in question The quantity in the parentheses can be thought of as the electric field at the point where the test object is placed
19. 19. Electric Field As with the electric force, if there are several charged objects, the net electric field at a given point is given by the vector sum of the individual electric fields i iEE 
20. 20. Electric Field r r dq kE ˆ2  If we have a continuous charge distribution the summation becomes an integral
21. 21. Hints 1) Look for and exploit symmetries in the problem. 2) Choose variables for integration carefully. 3) Check limiting conditions for appropriate result
22. 22. Electric Field Ring of Charge
23. 23. Electric Field Line of Charge
24. 24. Two equal, but opposite charges are placed on the x axis. The positive charge is placed at x = -5 m and the negative charge is placed at x = +5m as shown in the figure above. 1) What is the direction of the electric field at point A? a) up b) down c) left d) right e) zero 2) What is the direction of the electric field at point B? a) up b) down c) left d) right e) zero Example
25. 25. Example Two charges, Q1 and Q2, fixed along the x-axis as shown produce an electric field, E, at a point (x,y) = (0,d) which is directed along the negative y-axis. Which of the following is true? Q2 Q1 (c) E Q2 Q1 (b) E Q2 Q1 x y Ed (a) Both charges Q1 and Q2 are positive (b) Both charges Q1 and Q2 are negative (c) The charges Q1 and Q2 have opposite signs E Q2 Q1 (a)
26. 26. Electric Field Lines Possible to map out the electric field in a region of space An imaginary line that at any given point has its tangent being in the direction of the electric field at that point The spacing, density, of lines is related to the magnitude of the electric field at that point
27. 27. Electric Field Lines At any given point, there can be only one field line The electric field has a unique direction at any given point Electric Field Lines Begin on Positive Charges End on Negative Charges
28. 28. Electric Field Lines
29. 29. Electric Dipole An electric dipole is a pair of point charges having equal magnitude but opposite sign that are separated by a distance d. Two questions concerning dipoles: 1) What are the forces and torques acting on a dipole when placed in an external electric field? 2) What does the electric field of a dipole look like?
30. 30. Force on a Dipole Given a uniform external field Then since the charges are of equal magnitude, the force on each charge has the same value However the forces are in opposite directions! Therefore the net force on the dipole is Fnet = 0
31. 31. Potential Energy of a Dipole Given a dipole in an external field: Dipole will rotate due to torque Electric field will do work The work done is the negative of the change in potential energy of the dipole The potential energy can be shown to be EdqU 
32. 32. Electric Field of a Dipole