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Chapter 23F

# Chapter 23F - CHAPTER 23 The Electric Field II Continuous...

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CHAPTER 23 The Electric Field II: Continuous Charge Distributions 1* A uniform line charge of linear charge density λ = 3.5 nC/m extends from x = 0 to x = 5 m. ( a ) What is the total charge? Find the electric field on the x axis at ( b ) x = 6 m, ( c ) x = 9 m, and ( d ) x = 250 m. ( e ) Find the field at x = 250 m, using the approximation that the charge is a point charge at the origin, and compare your result with that for the exact calculation in part ( d ). ( a ) Q = λ L ( b ), ( c ), ( d ) E x ( x 0 ) = kQ /[ x 0 ( x 0 L )], Equ. 23-5 ( e ) E x kQ / x 2 Q = (3.5 × 10 –9 × 5) C = 17.5 nC E x (6) = 26.2 N/C; E x (9) = 4.37 N/C; E x (250) = 2.57 × 10 –3 N/C E x (250) = 2.52 × 10 –3 N/C, within 2% of ( d ) 2 Two infinite vertical planes of charge are parallel to each other and are separated by a distance d = 4 m. Find the electric field to the left of the planes, to the right of the planes, and between the planes ( a ) when each plane has a uniform surface charge density σ = +3 µ C/m 2 and ( b ) when the left plane has a uniform surface charge density σ = +3 µ C/m 2 and that of the right plane is σ = –3 µ C/m 2 . Draw the electric field lines for each case. ( a ) E = 4 π k σ = 3.39 × 10 5 N/C The field pattern is shown in the adjacent figure. The field between the plates is zero. ( b ) Again, E = 3.39 × 10 5 N/C. The field pattern is shown in the adjacent figure. The field is confined to the region between the two plates and is zero elsewhere. 3 A 2.75- µ C charge is uniformly distributed on a ring of radius 8.5 cm. Find the electric field on the axis at ( a ) 1.2 cm, ( b ) 3.6 cm, and ( c ) 4.0 m from the center of the ring. ( d ) Find the field at 4.0 m using the approximation that the ring is a point charge at the origin, and compare your results with that for part ( c ).

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