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Unformatted text preview: hysics 2B  Summer Session 2  C. Palmer y θ
R z R0 August 7, 2013 18 z There is a ring of charge, Q, in the z=0 plane.
The ring has radius, R0. x dEz dE dER Set up dEz quantitatively Ez =
= kE (R 2
0 kE z
+z 2 ) 3 2 (R +z 2 ) 3 0 dq θ
R zQ
2
0 ∫ Q 2 y dq=λdl Physics 2B  Summer Session 2  C. Palmer z R0 August 7, 2013 19 z The ring of charge from the previous example will be the small piece that we
integrate over to find the total electric
field.
The disk has radius, R0, and has total
charge Q. dEz ( r ) x y z R0 r Physics 2B  Summer Session 2  C. Palmer August 7, 2013 20 The ring has radius, R0. What is the charge
dEz
density of the DISK?
A) QC
σ=
2
2
π R0 m z (r ) x y B) QC
σ= 2 2
πr m
z C) QC
λ=
2π R0 m D) QC
λ=
2π r m Physics 2B  Summer Session 2  C. Palmer R0 r August 7, 2013 21 The ring has radius, R0. What is the charge
dEz
density of the DISK?
A) QC
σ=
2
2 R0 m z (r ) x y B) QC
σ= 2 2
πr m
z C) QC
λ=
2π R0 m D) QC
λ=
2π r m Physics 2B  Summer Session 2  C. Palmer R0 r August 7, 2013 22 z Given that the charge density of the disk, what is the total charge of a ring with
radius, r, and thickness, dr? () Q
2
qring =
π r dr
2
A)
π R0
Q
rdr
2
B) qring =
π R0
Q
2π r ) dr
C) qring =
2(
π R0
Q
2
D) q =
π ( dr )
ring
2
π R0 x y dEz ( r ) Q
σ=
2
π R0 Physics 2B  Summer Session 2  C. Palmer z R0 r August 7, 2013 23 z Given that the charge density of the disk, what is the total charge of a ring with
radius, r, and thickness, dr? () Q
2
qring =
π r dr
2
A)
π R0
Q
rdr
2
B) qring =
π R0
Q
2π r ) dr
C) qring =
2(
π R0
Q
2
D) q =
π ( dr )
ring
2
π R0 x y dEz ( r ) Q
σ=
2
π R0 Physics 2B  Summer Session 2  C. Palmer z R0 r August 7, 2013 24 z The disk has radius, R0, and has total dE ( r )
z x y charge Q.
Now we are ready to write the electric
field from each ring. z R0 r Physics 2B  Summer Session 2  C. Palmer August 7, 2013 25 z The disk has radius, R0, and has total dE ( r )
z x y charge Q.
Now we are ready to write the electric
field from each ring. dE z ( r ) = k E
= kE ( zqring
r +z
2 z (r 2 +z 2 ) 3 2 2 ) 3 2 σ ( 2π r ) dr Physics 2B  Summer Session 2  C. Palmer z R0 r August 7, 2013 26 z The disk has radius, R0, and has total dE ( r )
z x y charge Q.
Now we are ready to write the electric
field from each ring. dEz (r ) = kEπ zσ ( 2r ) dr (r 2 +z 2 ) z
3 2 R0 r Physics 2B  Summer Session 2  C. Palmer August 7, 2013 27 z The disk has radius, R0, and has total dE ( r )
z x y charge Q.
Now we are ready to write the electric
field from each ring. Ez = kEπ zσ ∫ 2rdr r = R0 r =0 (r 2 +z 2 )...
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This note was uploaded on 09/10/2013 for the course PHYS 2B 2b taught by Professor Hirsch during the Summer '10 term at UCSD.
 Summer '10
 Hirsch

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