electric field formulas for several continuous distribution of charge
DESCRIPTION
The Electric Field of a Dipole We can represent an electric dipole by two opposite charges ±q separated by the small distance s. The dipole moment is defined as the vector The dipole-moment magnitude p = qs determines the electric field strength. The SI units of the dipole moment are C m.TRANSCRIPT
![Page 1: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/1.jpg)
Chapter 27: 4-5
Electric Field formulas for several continuous distribution of charge.
![Page 2: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/2.jpg)
We can represent an electric dipole by two opposite charges ±q separated by the small distance s.The dipole moment is defined as the vector
The Electric Field of a Dipole
The dipole-moment magnitude p = qs determines the electric field strength. The SI units of the dipole moment are C m.
![Page 3: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/3.jpg)
The electric field at a point on the axis of a dipole isThe Electric Field of a Dipole
where r is the distance measured from the center of the dipole.The electric field in the plane that bisects and is perpendicular to the dipole is
This field is opposite to the dipole direction, and it is only half the strength of the on-axis field at the same distance.
![Page 4: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/4.jpg)
Problem-Solving Strategy: The electric field of a continuous distribution of charge
![Page 5: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/5.jpg)
Problem-Solving Strategy: The electric field of a continuous distribution of charge
![Page 6: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/6.jpg)
Problem-Solving Strategy: The electric field of a continuous distribution of charge
![Page 7: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/7.jpg)
Example 26.3Derivation on pages 827-828
![Page 8: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/8.jpg)
See appendix A-3 for integral
Derivation on pages 827-828
![Page 9: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/9.jpg)
Electric Field of a infinite line of charge
Electric Field of a line of charge
2L to reduces radical then L
2LrrQ
41E
220rod
![Page 10: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/10.jpg)
![Page 11: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/11.jpg)
Electric Field on Ring
232204
1RzzQE
xring
2/322
0
12/322
01
2/3220
22220
22
22
20
41
41
4141
cos
cos41cos
RzzQE
QRzzEE
QRzzE
Rzz
RzQE
Rz
zrzRzr
rQEE
zring
N
i
N
iizz
iz
iz
ii
i
ii
iiiz
![Page 12: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/12.jpg)
A Disk of Charge
![Page 13: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/13.jpg)
Electric Field of a disk of charge
220
02/322
0
12/322
0
1 12/322
0
12
2)(
,
2
2
4
Rz
zzE
rz
rdrzE
drrNrz
rrzE
rrAQrz
QzEE
zdisk
R
zdisk
N
i i
izdisk
ii
N
i
N
i i
zizdisk
![Page 14: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/14.jpg)
The on-axis electric field of a charged disk of radius R, centered on the origin with axis parallel to z, and surface charge density η = Q/πR2 is
A Disk of Charge
NOTE: This expression is only valid for z > 0. The field for z < 0 has the same magnitude but points in the opposite direction.NOTE 2: The formula reduces to a plane of charge relationship at R>>z
![Page 15: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/15.jpg)
A Plane of ChargeThe electric field of an infinite plane of charge with surface charge density η is:
For a positively charged plane, with η > 0, the electric field points away from the plane on both sides of the plane.For a negatively charged plane, with η < 0, the electric field points towards the plane on both sides of the plane.
Formula above can be derived from charge disk formula, see page 830.
![Page 16: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/16.jpg)
![Page 17: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/17.jpg)
The Parallel-Plate Capacitor• The figure shows two electrodes, one with charge +Q and the other with –Q placed face-to-face a distance d apart. • This arrangement of two electrodes, charged equally but oppositely, is called a parallel-plate capacitor. • Capacitors play important roles in many electric circuits.
![Page 18: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/18.jpg)
The electric field inside a capacitor is
where A is the surface area of each electrode. Outside the capacitor plates, where E+ and E– have equal magnitudes but opposite directions, the electric field is zero.
The Parallel-Plate Capacitor
Use two infinite size disks to create the relationship for a capacitor. If z <<R, second fraction reduces to 0. Since there are 2 disks, then formula is doubled.
![Page 19: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/19.jpg)
EXAMPLE 27.7 The electric field inside a capacitor
QUESTIONS:
![Page 20: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/20.jpg)
EXAMPLE 27.7 The electric field inside a capacitor
![Page 21: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/21.jpg)
EXAMPLE 27.7 The electric field inside a capacitor
![Page 22: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/22.jpg)
EXAMPLE 27.7 The electric field inside a capacitor
![Page 23: Electric Field formulas for several continuous distribution of charge](https://reader035.vdocuments.us/reader035/viewer/2022062302/5a4d1afa7f8b9ab059983738/html5/thumbnails/23.jpg)
A sphere of charge Q and radius R, be it a uniformly charged sphere or just a spherical shell, has an electric field outside the sphere that is exactly the same as that of a point charge Q located at the center of the sphere:
A Sphere of Charge