1. 22-4 The Electric Field Due to a Point Charge
جامعة أم القري
كلية العلوم التطبيقية للبنات
22-2 The Electric Field
22-3 Electric Field Lines
22-4 The Electric Field Due to a Point Charge
22-8 A Point Charge in an Electric Field
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2. The Electric Field
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3. The Coulomb’s law tells us how a charged particle interacts with another charged particle.?
How does particle 1 “know” of the presence of particle 2? That is, since the particles do not touch, how can particle 2 push on particle 1—how can there be such an action at a distance?
The concept of Electric Field is introduced to explain this question.
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4. The explanation that we shall examine here is this: Particle 2 sets up an electric field at all points in the surrounding space, even if the space is a vacuum. If we place particle 1 at any point in that space, particle 1 knows of the presence of particle 2 because it is affected by the electric field particle 2 has already set up at that point. Thus, particle 2 pushes on particle 1 not by touching it as you would push on a coffee mug by making contact. Instead, particle 2 pushes by means of the electric field it has set up.
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5. The direction of force defines the direction of field
The electric field is a vector field. It consists of a distribution of vectors, one for each point in the region around a charged object.
The direction of force defines the direction of field
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6. The electric field E at any point is defined in terms of the electrostatic force F that would be exerted on a e test charge q0 placed there:
SI Unit of Electric Field: newton per coulomb (N/C)
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7. Electric Field Lines
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8. In order to understand the electric filed better, we will try to visualize the electric field now.
Michael Faraday introduced the idea of electric fields in the 19th century and thought of the space around a charged body as filled with electric field lines .
The direction of the field lines indicate the direction of the electric force acting on a positive test charge.
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9. A closer spacing means a larger field magnitude.
The electric field vector at any point is tangent to the field line through that point
The density of the field lines is proportional to the magnitude of the field.
A closer spacing means a larger field magnitude.
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10. Electric field lines extend away from positive charge (where they originate) and toward negative charge (where they terminate). q
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11.
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12. 22-4 The Electric Field Due to a Point Charge
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13. The electric field due to a point charge q is:
From Coulomb’s law, the electrostatic force due to q, acting on a positive test charge q0 is:
The electric field due to a point charge q is:
The field of a positive point charge is shown on the right, in vector form.
The magnitude of the field depends only on the distance between the point charge (as the field source) and the location where the field is measured.
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14. Electric field is a vector quantity.
Thus, the net, or resultant, electric field due to more than one point charge is the superposition of the field due to each charge.
The net electric field at the position of the test charge, due to n point charges, is:
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15. Ex = E1x + E2x + E3x +E4x Ey = E1y + E2y + E3y +E4y 1436-1437
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16. Checkpoint 1 Rightward Leftward Leftward Rightward
The figure here shows a proton p and an electron e on
an x axis.What is the direction of the electric field due to the electron at (a) point S and
(b) point R?
What is the direction of the net electric field at (c) point R and (d) point S?
The direction of the electric field due to the electron at:
(a) Point S?
Point R?
The direction of the net electric field at
(c) Point R?
(d) Point S?
Rightward
Leftward
Leftward
Rightward
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17. Sample Problem
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18. Figure 22-7a shows three particles with charges q1=+2Q, q2 = -2Q, and q3=-4Q, each a distance d from the origin. What net electric field is produced at the origin?
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19. To find the magnitude of which is due to q1, we use Eq
To find the magnitude of which is due to q1, we use Eq. 22-3, substituting d for r and 2Q for q and obtaining
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20. 22-8 A Point Charge in an Electric Field
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21. If a particle with charge q is placed in an external electric field E, an electrostatic force F acts on the particle:
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22. Measuring the Elementary Charge
Equation played a role in the measurement of the elementary charge e by American physicist Robert A. Millikan in 1910–1913. When tiny oil drops are sprayed into chamber A, some of them become charged, either positively or negatively, in the process. Consider a drop that drifts downward through the small hole in plate P1 and into chamber C.
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23. Millikan discovered that the values of q were always given by
in which e turned out to be the fundamental constant we call the elementary charge
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24. Ink-jet printer. Drops shot from generator G receive a charge in charging unit C. An input signal from a computer controls the charge and thus the effect of field E on where the drop lands on the paper.
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25. (a) leftward
(b) leftward
(c) decrease
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26. Electric Dipole
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27. An electric dipole consists of two particles with charges of equal magnitude q but opposite signs, separated by a small distance d.
The magnitude of the electric field set up by an electric dipole at a distant point on the dipole axis (which runs through both particles) can be written in terms of either the product qd or the magnitude p of the dipole moment:
where z is the distance between the point and the center of the dipole.
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28.
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29.
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30. (The unit of electric dipole moment is the coulomb-meter.)
The product qd, which involves the two intrinsic properties q and d of the dipole, is the magnitude p of a vector quantity known as the electric dipole moment of the dipole.
(The unit of electric dipole moment is the coulomb-meter.)
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31. 22-7 A Dipole in an Electric Field
The torque on an electric dipole of dipole moment p when placed in an external electric field E is given by a cross product:
A potential energy U is associated with the orientation of the dipole moment in the field, as given by a dot product:
An electric dipole in a uniform external electric field E. Two centers of equal but opposite charge are separated by distance d. The line between them represents their rigid connection.
Field E: causes a torque τ on the dipole. The direction of τ is into the page, as represented by the symbol (x-in a circle) .
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32. Electrostatic forces act on the charged ends of the dipole
Electrostatic forces act on the charged ends of the dipole. Because the electric field is uniform, those forces act in opposite directions (as shown in Fig a) and with the same magnitude F = qE. Thus, because the field is uniform, the net force on the dipole from the field is zero and the center of mass of the dipole does not move
the forces on the charged ends do produce a net torque on the dipole about its center of mass. The center of mass lies on the line connecting the charged ends, at some distance x from one end and thus a distance (d - x ) from the other end.
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33. we can write the magnitude of the net torque as:
We can generalize this equation to vector form as
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34. Potential energy can be associated with the orientation of an electric dipole in an electric field. The dipole has its least potential energy when it is in its equilibrium orientation, which is when its moment p: is lined up with the field E
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35. If the change in orientation is caused by an applied torque (commonly said to be due to an external agent), then the work Wa done on the dipole by the applied torque is the negative of the work done on the dipole by the field; that is
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36.
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37. all tie; (b) 1 and 3 tie, then 2 and 4 tie 1436-1437
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38.
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39.
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40.
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41.
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42.
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43. 22 Summary Definition of Electric Field
The electric field at any point
Field due to an Electric Dipole
The magnitude of the electric field set up by the dipole at a distant point on the dipole axis is
Eq. 22-1
Eq. 22-9
Electric Field Lines
provide a means for visualizing the directions and the magnitudes of electric fields
Field due to a Point Charge
The magnitude of the electric field E set up by a point charge q at a distance r from the charge is
Eq. 22-3
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44. 22 Summary Force on a Point Charge in an Electric Field
When a point charge q is placed in an external electric field E
Dipole in an Electric Field
The electric field exerts a torque on a dipole
The dipole has a potential energy U associated with its orientation in the field Eq Eq Eq
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45. Tutorial
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46. Since the charge is uniformly distributed throughout a sphere, the electric field at the surface is exactly the same as it would be if the charge were all at the center. That is, the magnitude of the field is
where q is the magnitude of the total charge and R is the sphere radius.
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47. (b) The field is normal to the surface and since the charge is positive, it points outward from the surface.
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48.
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49.
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50. (b) This field points at 45.0°, counterclockwise from the x axis.
By symmetry we see that the contributions from the two charges q1 = q2 = +e cancel each other, and we simply use Eq to compute magnitude of the field due to q3 = +2e.
(a) The magnitude of the net electric field is
(b) This field points at 45.0°, counterclockwise from the x axis.
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51.
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52. (a) The linear charge density is the charge per unit length of rod
(a) The linear charge density is the charge per unit length of rod. Since the charge is uniformly distributed on the rod,
(b) We position the x axis along the rod with the origin at the left end of the rod, as shown in the diagram.
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53. The total electric field produced at P by the whole rod is the integral
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54.
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55.
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56.
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57. The magnitude of the force acting on the electron is F = eE, where E is the magnitude of the electric field at its location. The acceleration of the electron is given by Newton’s second law:
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58. (a) The magnitude of the dipole moment is
(b) Following the solution to part (c) of Sample Problem — “Torque and energy of an electric dipole in an electric field,” we find
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59. Home work
No. 2, 56, and 83
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