Phys2212_L04

# Phys2212_L04 - Physics 2212 Electricity and Magnetism...

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Physics 2212 Electricity and Magnetism Lecture 4 Computing Electric Fields

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10/06/09 Physics 2212 - Lecture 4 2 weak strong Review of Field Lines Q 2Q -Q More charge more field lines. Field lines stop on negative charges. start positive charges. Field lines never cross. Field line spacing indicates field strength + + + Closed loops? Energy flow.
10/06/09 Physics 2212 - Lecture 4 3 Recall : Computing Charged Object E-Fields Using Coulomb’s Law 1. Choose a coordinate system that will facilitate integration. 2. Use any applicable symmetries to set E-field components to zero or equal to each other. 3. Break up the object into point-like elements. 4. Write the Coulomb’s Law contribution to the E-field from a representative point-like element. 5. Integrate over the entire object to get the E-field.

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10/06/09 Physics 2212 - Lecture 4 4 Recall: The E-Field of a Charged Ring A thin uniformly charged ring of radius R has a total charge Q . Find the electric field on the axis of the ring . . the z-axis (perpendicular to the page). The linear charge density of the ring is λ = Q /(2 π R ). The system has cylindrical symmetry for rotations about the axis, so along the z-axis E x =E y =0 and we need only to find E z . Consider a small segment of the circumference of the ring of width dl = R d φ . The contribution to the electric field on the z-axis is : 2 2 2 2 2 0 0 1 1 cos 4 4 z i dQ Rd z dE r R z R z λ θ πε = = + + ( 29 ( 29 ( 29 2 3/ 2 3/ 2 2 2 2 2 0 0 0 3/ 2 2 2 0 1 1 4 2 1 4 z Rz Rz E d R z R z Qz R z π ε = = + + = +
10/06/09 Physics 2212 - Lecture 4 5 The on-axis E-Field of a Charged Ring (2) 3 0 1 ( ) 4 z Qz E z R R πε << = 2 0 1 ( ) 4 z Q E z R z = ( 29 3/ 2 2 2 0 1 4 z Qz E R z = + Near-field limit: linear Far-field limit: 1/r 2

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10/06/09 Physics 2212 - Lecture 4 6 Example: A Charged Ring A thin uniformly charged ring of radius R = 0.1 m has a total charge Q = 10 nC. Find the electric field on the axis of symmetry at z = 0.2 m from the center the ring. ( 29 3/ 2 2 2 0 -8 9 2 2 2 2 3/ 2 3 1 4 (1.0 10 C)(0.2 m) (9.0 10 N m /C ) [(0.1 m) (0.2 m) ] 1.61 10 N/C z Qz E R z πε = + × = × + = ×
10/06/09 Physics 2212 - Lecture 4 7 The E-Field of a Charged Disk A thin uniformly charged disk of radius R has a total charge Q . Find the electric field E at points on the z axis perpendicular to the disk plane. The charge area-density of the disk is η = Q/A = Q/( π R 2 ) . It has cylindrical symmetry for rotations about the z axis, so E x =E y =0 , and we need only find E z Consider the disk to be made of successive rings, each having radius r , thickness dr , and charge dQ= η (2 π rdr ) Then the contribution of each ring to E z

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## This note was uploaded on 06/07/2009 for the course PHYSICS 2212 taught by Professor Geist during the Fall '09 term at Georgia Perimeter.

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Phys2212_L04 - Physics 2212 Electricity and Magnetism...

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