1 LOGO Chapter 5 Electric Field in Material Space Part 1 iugaza2010.blogspot.com Materials: (1)Conductor σ>>1 (2) Insulator (or dielectric) σ<<1 (3) Semiconductor Conductivity(σ) the measure of the ability of material to conduct current (mho/m) (S/m) ,depends on: temperature and frequency. 3 dq Current : I dt I 2 Current density : J (A/m ) S and I J.dS Perfect Conductor( ) R 0 , E 0 , v 0(inside) Perfect Insulator( 0) R ,J 0 4 Convection Current doesn' t apply ohm' s law occurs when current flow in insulating medium J vu u : change velocity Conduction Current occurs when current flow in conducting medium J E 5 A conductor of uniform cross section under an applied E field V E.dl V E l I V J E S l I V S l V l R I S R l S c l S 1 where c is the resestivity I J S 6 For non uniform cross section V R I E.dl E.dS 7 For current density J=10zsin2Ф aρ A/m2 Find the current through the cylindrical surface: ρ=2 ,1≤ z ≤ 5m I J .dS , dS ddz a 5 2 I 10z sin 2 ddz z 1 0 5 2 20z sin 2 ddz z 1 0 I 240 754 A 8 For convective charge transport A=0.1m2, u=10 m/s , R=1014 Ω , ρs=0.5 μc/m2 Find the potential difference. V J s u I s uA s uA R 6 14 V s uAR (0.5 *10 )(10)(0.1)(10 ) 50MV 9 The free charge density in copper is 1.81*1010 c/m3 for current density 8*106 A/m2 , σ=5.8*107 S/m Find the electric field intensity and drift velocity . v 1.8110 c / m 10 J 8 10 A / m 6 J v u u 3 2 J 4 4.42 10 m / s v J J E E 0.138N / c 10 A lead(σ=5*106 S/m) bar of square cross section has a hole bored a long its length of 4m and filled with copper (σ=5.8*106 S/m) Determine the resistance of the composite bar. R Lead l L AL R copper l c Ac 4 2 0.01 6 2 (5 10 ) (0.03) 2 9.74 104 4 3 8 . 7 10 2 0.01 6 (5.8 10 ) 2 Rtot R Lead || R copper R Lead R copper R Lead R copper 8.759104 11 Determine the total current in a wire of radius 1.6mm if J=500/ρ az A/m2 placed along Z-axis. I J .dS , dS dd a z 2 1.6 mm I 0 0 500 dd 5.026 A 12 The charge 10-4 e-3t C is removed from a sphere through a wire. Find the current in the wire at t=0 and t=2.5s . dq 4 3t I (3)10 e dt 4 I (t 0) 3 10 A 4 I (t 1) 3 10 e 3 ( 2 .5 ) 9 166 10 A 13 R=1MΩ , l=2m , r=4mm (cylinder) Determine the conductivity. R l A l 0.02 4 3.97810 S / m 6 2 R A (10 )( 0.004 ) 14 Cylindrical bar of Carbon (σ=3*104 S/m) of radius 5mm and length 8cm are maintained at potential difference of 9V , find (a) The resistance of the bar. (b) The current through the bar. (c) The power dissipated in the bar. 2 8 10 3 (a) R 34 10 S / m 4 2 A (3 10 )( 0.005 ) V 9 (b) I 265A 3 R 34 10 2 2 3 (c) P I R (265) (34 10 ) 2387.7W 15 l The resistance of a long wire of diameter 3mm is 4.04 Ω/km if I=40A find (a)σ (b)J l 1000 7 (a) 3.7 10 S / m 2 R A (4.04)( 0.0015 ) I 40 6 2 (b) J 5.65 10 A / m 2 S 0.0015 16 A coil is made of 150 turns of copper wound on a cylindrical core. If the mean radius of the turn is 6.5mm and the diameter of the wire is 0.4mm calculate the resistance of the coil. L 2 (6.5 103 )(150) 6.1261m L 6.1261 R 0.84 2 A 0.4 103 (5.8 107 ) 2 17 A hollow cylindrical of length 2m has its cross section as in fig. If the cylinder is made of carbon (σ=3*104 S/m) . Determine the resistivity between the ends of the cylinder. A 5 10 2 2 3 10 2 2 5.02 10 2 m 2 L 2 R 1.328 4 2 A (3 10 )(5.02 10 ) 18 A composite conductor 10m long consist of an inner core of steel of radius 1.5cm and an outer sheath of copper whose thickness is 0.5cm (σcopper=5.8*107 S/m) , (σsteel=8.4*106 S/m) . (a) Determine the resistance of the conductor. L1 10 R steel 1 A1 (8.4 106 ) 1.5 10 2 Cop. 2 St. 1.67 103 L2 10 R copper 2 A2 (5.8 107 ) 2 102 2 1.5 102 2 3.136104 19 Rtot R steel || R copper R steel R copper R steel R copper 2.64 104 (b) If the total current in the conductor is 60A what current flows in each metal? 60( Rs ) Ic (current divider) Rc Rs (60)(1.67 103 ) 50.51A 3 4 (1.67 10 ) (3.136 10 ) Is 60 50.51 9.48 A 20 LOGO iugaza2010.blogspot.com melasmer@gmail.com 21