isaac newton (1642–1727) physics 2113 lecture 06: mon 8 oct
TRANSCRIPT
![Page 1: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/1.jpg)
Physics 2113 Lecture 06: MON 8 OCT
CH22: Electric Fields
Physics 2113
Michael Faraday (1791–1867)
Isaac Newton (1642–1727)
![Page 2: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/2.jpg)
2q−12F1q+ 21F
12r
Coulomb’s law
212
2112
||||||rqqkF =
2
212
00
1085.8with 41
mNCk −×== επε
2
291099.8CmN
×k =
For charges in a VACUUM
Often, we write k as:
Electric forces are added as vectors.
![Page 3: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/3.jpg)
Electric Fields • Electric field E at some point in space is defined as the force divided by the electric charge.
• Force on charge 2 at some point, by charge 1 is given by
• Electric field at that point is
21
12||||
RqkE =
!
EqF!!
=
221
12||||||
RqqkF =
!
![Page 4: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/4.jpg)
Field lines Useful way to visualize electric field. They start at a positive charge, end at negative charge. At any point in space electric field is tangential to field line. Field is proportional to how “packed” the lines are.
![Page 5: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/5.jpg)
Example
The electric field lines on the le= have twice the separa?on as those on the right. If the magnitude of the field at A is 40 N/C, what is the magnitude of field at B?
![Page 6: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/6.jpg)
Charge q1 on inner spherical shell, -‐q2 on outer. Sketch the field lines.
![Page 7: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/7.jpg)
Electric field of a point charge
F!"= k qq0
r2 r̂,
where r̂ is a unit radial vector.
To compute electric field of more than one charges, one should try to simplify the problem by breaking it to simpler problem.
ˆ 32 rrq
krrq
kE !==
![Page 8: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/8.jpg)
Example • 4 charges are placed at the
corners of a square as shown. • What is the direction of the
electric field at the center of the square?
(a) Field vanishes at the center (b) Along +y (c) Along +x
-q
-2q
+2q
+q
y
x
![Page 9: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/9.jpg)
![Page 10: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/10.jpg)
Two par?cles are fixed to an x axis: par?cle 1 of charge q1=2.1x10-‐8 C at x=20cm and par?cle 2 of charge q2=-‐4q1 at x=70cm. At what coordinate on the axis is the net electric field zero?
![Page 11: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/11.jpg)
To simplify things, we only compute the field along the axis.
P d
x
What is the electric field at P due to the dipole?
q− q+
_E :fields ofion Superposit EE!!!
+= +
,
241
20
⎟⎠
⎞⎜⎝
⎛ −
=+dx
qEπε
!2
0
241
⎟⎠
⎞⎜⎝
⎛ +
−=−dx
qEπε
!
Electric field due to a dipole
![Page 12: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/12.jpg)
When x>>d, at distances much greater than the dipole
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ +−⎟⎠
⎞⎜⎝
⎛ −=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎟⎠
⎞⎜⎝
⎛ +
−
⎟⎠
⎞⎜⎝
⎛ −
=−− 22
022
0 2242
1
2
14
dxdxqdxdx
qEπεπε
!
12
12
22
22
⎟⎠
⎞⎜⎝
⎛ +=⎟⎠
⎞⎜⎝
⎛ ±=⎟⎠
⎞⎜⎝
⎛ ± −−
−−
!∓xdx
xdxdx
Then
30
20
20 2
24
114 x
qdxd
xq
xd
xd
xqE
πεπεπε==⎥
⎦
⎤⎢⎣
⎡⎟⎠
⎞⎜⎝
⎛ +−−⎟⎠
⎞⎜⎝
⎛ ++= !!"
• Since, 2d << x, the field is weaker than that of the point charge at large x. • Field scales with charges, vanishes if 0→d
![Page 13: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/13.jpg)
Electric Dipole Moment
30
30 22 x
px
qdEπεπε
==
Using expression for the electric field of the dipole, we find
The direction of dipole moment is taken from negative to positive charge.
![Page 14: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/14.jpg)
The electric quadrupole It consists of two dipoles of equal magnitude place close to each other and in opposite direc?ons.
The story can be con?nued: superposed two quadrupoles, obtain an octupole… hexadecupole… All with fields that decay faster and faster with distance.
![Page 15: Isaac Newton (1642–1727) Physics 2113 Lecture 06: MON 8 OCT](https://reader030.vdocuments.mx/reader030/viewer/2022012019/616881ebd394e9041f700c87/html5/thumbnails/15.jpg)
Summary
• Electric is a property of space that characterizes how charges placed in it react to it.
• Field lines are a quick way to visualize fields.
• In dipoles and higher multipoles, the leading contribution to the fields cancel, leading to faster dropoff with distance in the magnitude of the fields.