Chapter 22 Magnetic Forces and Magnetic Fields 2 Fig. 22-CO, p. 727.
22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !!...
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Transcript of 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !!...
![Page 1: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/1.jpg)
22-1 Charges and Forces: A closer look:
Why fields?
To explain “action at a distance”!!
Chapter 22: Electric Fields
Introduction:
What do we really want to get out of chapter 23?
Review: vectors!
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22-2 The Electric Field (E):
To find the field (E) at a location (P) due to a charge q, calculate:
E = F/q0
where q0 is a “test charge” places at P.
The units of E is N/C.
Typical fields:
At hydrogen nucleus surface: 1011 N/C
At surface of photocopier drum: 105 N/C
Near a charged comb: 103 N/C
In copper wire circuits: 10-2 N/C
![Page 3: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/3.jpg)
22-3 Electric Field Lines:
Are merely to visualize patterns in electric fields.
1- The direction of the tangent to the field lines at any point is the direction of E at that point.
2- The number of lines per unit area is proportional to the magnitude of E.
![Page 4: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/4.jpg)
Example:
1- A single (positive or negative) point charge.
2- A charged conducting sphere.
3- Two (like or unlike) point charges.
4- A charged slab (or sheet) [finite or infinite]
5- A charged line (or cylinder) [short or long]
Note that electric field lines originate at positive charges (or at infinity) and terminate at negative charges (or at infinity).
![Page 5: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/5.jpg)
No two fields lines can cross or touch.
Field lines are not material objects.
Although the lines are drawn as discrete, the field itself is continuous.
![Page 6: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/6.jpg)
22-4 Electric Field Due to a Point Charge:
For a charge q:
|F| = k |q| |q0|/r2
Therefore,
E = k |q|/r2 point away from q if q is positive
E = k |q|/r2 point toward q if q is negative
If there are many charges q1, q2, q3, …, qn:
Use “superposition”: the net field is the vector sum of the fields due to each of the n charges.
![Page 7: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/7.jpg)
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Away from qj if qj is positive; toward qj if qj is negative!
E = F/q0 =E1 + E2 + … + En
Check point 1:
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If we want to find the electric field due to a dipole at a point which is a distance z away from the midpoint between the two dipole charges, then:
Edipole = E+ + E-
p is called the electric dipole moment; its magnitude is: q · d, where d is the distance between the two charges.
22-5 E Due to an Electric Dipole:
p is a vector that points from the negative charge to the positive charge.
![Page 9: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/9.jpg)
What are the SI units of p?
Interaction: prove it!!
Along the dipole axis, when z >> d, one finds that:
Edipole = 2k p/z3
and is directed along the dipole axis.
Note that, for large distances, Edipole ~ p (not q alone or d alone); also E ~ 1/r3 not 1/r2!!
![Page 10: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/10.jpg)
22-8 A point charge in E:
When a point charge q is places in a field E, the force experienced by this charge is:
F = q E
Applications: (see H&R pg. 533)
1- Millikan oil-drop experiment: q = n e
2- Ink-jet printing
3- Volcanic lightning
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Solve sample problem 23.4 (pg. 534)
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22-9 A dipole in in E:
H2O ~ an electric dipole… why?
For a uniform E:
Fnet = 0
But the torque ():
= p x E
The torque tends to rotate p into the direction of E!!
![Page 13: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/13.jpg)
What is the potential energy in a dipole field?
The change in potential energy is the negative of the work done by field on the dipole.
θ
θr
θrθ dθ τUU Compare with gravitational potential energy
Taking r = 90o, U(r) = 0
Therefore:
U() = - p E cos = - p · E
![Page 14: 22-1 Charges and Forces: A closer look: Why fields? To explain “ action at a distance ” !! Chapter 22: Electric Fields Introduction: What do we really.](https://reader036.fdocuments.us/reader036/viewer/2022082403/56649e035503460f94aee327/html5/thumbnails/14.jpg)
Therefore, the work done by the field on the dipole is:
W = -U = Ui – Uf
However, the applied work by an external agent is:
Wagent = Uf – Ui
Solve problem: