HW-5Solutions-01-23-08 - Physics 21 Spring 2008 HW-5...

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Physics 21 Spring 2008 January 23, 2008 HW-5 Solutions 5-1. (HRW 24-7) An infinite nonconducting sheet has a surface charge density . (a) How much work is done by the electric field due to the sheet if a particle of charge is moved from the sheet to a point P at distance d = 3.56 cm from the sheet? (b) If the electric potential V is defined to be zero on the sheet, what is V at P? Solution: (a) The work done by the electric field is 19 12 2 0 0 0 12 2 2 0 0 0 21 (1.60 10 C)(5.80 10 C/m )(0.0356 m) 2 2 2(8.85 10 C /N m ) 1.87 10 J. f d i q q d W q E ds dz σ σ ε ε × × = = = = × = × r r (b) Since V – V 0 = – W / q 0 = – σ z /2 ε 0 , with V 0 set to be zero on the sheet, the electric potential at P is 12 2 2 12 2 2 0 (5.80 10 C/m )(0.0356 m) 1.17 10 V. 2 2(8.85 10 C /N m ) z V σ ε × = − = − = − × × 5-2 . (HRW 24-13) What are (a) the charge and (b) the charge density on the surface of a conducting sphere of radius 0.15 m whose potential is 200 V (with at infinity)? Solution: (a) The charge on the sphere is 9 0 9 2 2 (200 V)(0.15 m) 4 3.3 10 C.
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