Added the radial component will sum to zero because

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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.

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