quiz5-solutions

# quiz5-solutions - ECE 220 — Quiz 5 (04/12/04) Please...

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Unformatted text preview: ECE 220 — Quiz 5 (04/12/04) Please write your name at the top right corner before you start the exam Remember to write the units of the various quantities that you calculate Use the back side of each page if you need extra space. All formulas and units that you need are given on the last page 1. Calculate the magnetic ﬁeld (H) and the magnetic ﬂux density due to a coaxial cable in the regions: C ‘2— 0 PO" M75) a) a < r < b (between the conductors) b) r > c (outside the cable) I (Figure below shows a cross—section of the cable). A current I (A) ﬂows through the inner conductor (into the paper) and an equal and opposite current ﬂows through the outer conductor i.e. I (A) out of the paper. The material between the conductors has a permeability uo. Assume the cable is inﬁnitely long and perfectly cylindrical. Please indicate the direction of the magnetic ﬁeld in both cases. Re ioi’) l: CLAY-4b I \\ Q U?) H O .0 a N0 MO-gf’Q/HC Vidal Omtsiol the Coaxial Cable/- 2. A Power device made of silicon carries a current of 100A. The size of the device is 10mm X 10mm and is 1mm thick. The potential drop on the device is 0.6 volts. ( I 5 Poi 0 b5) . a) What is the conductivity of the silicon used? (V = Ed) Tthkness b) If the velocity of the carriers is ZOOOm/s, how many free charges (electrons) per unit volume must be present in the device? Area (10mm x 10mm) through which the current is ﬂowing (a) Condmchvlhj 0" : Edam/inert? densiI—a i E A) elecWiC Field __3 : [00x |XIO : wag/Q eye >< (0’4 ” 4-3 L) aveot ((00% Voltage ‘ MO mm) :(O'lf ml, ~l V:9»XlOg 07/5 r7: ? Charge; 0p : [,6Xlg cl 7 M aleol’TOn I e nay/VA ('1 t; I : IOO ﬂ/VA loexm'qu Elwogxtod‘ : 34.25 X{ORI (alccl-fonS/mg) 3. The magnetic field at the interface between two mediums is as shown below. Assuming there is no current ﬂowing on the interface. ( I 5 poi n t5) tan 0:1 _ h tan a 2 i” 2 . (Hint: Write out your boundary conditions in terms of H1 and H2) Prove Hnl H1 Medium 1 Permeability — u; m Htl Boundary Ha 012 Medium 2 Permeability — u; H2 Hn2 H“. g H, (/08 (X, Hnz ; H1 cos o<7_ ' ‘ g ‘l n 0( He‘ .— l’i'Sln 0(‘ H152 2 Using 2CD g '8’) ,7; “HIM:HHn‘ﬁnHlCOSOS:yH’COSD<’ " l n; 1 , Ht: : Ht, :9 Miami: H.smo<. 4 @ (Since K350) . no a vmrc at" the bOM'ndQV‘CL! Léhd/{HOHS E E" 3 52 r) i 3: ‘L‘ , 3 Li \H/ d— 9 t) R N \ fr 1% R List of units 1) Current — Amperes (A) 2) Current Density (I) — Amperes/meter2 (A / m2) 3) Magnetic Field — Amperes /meter(A / m) 4) Magnetic Flux Density — Tesla (T) 5) Permeability (u) — Henry/ meter (H / m) 6) Conductivity — Siemens (S) List of formulas and quantities 1) Maxwell’s equations (for magnetism) VE = 0 6 x H = j + — 2) Gauss’s law for magnetic ﬁelds: B .d S = 0 3) Circumference of a circle of radius ‘R’(m) — 27: R (m) 4) Ampere’s law: = [we 6) Boundary conditions for magnetic ﬁelds at any interface Bug — Bnl = 0 (normal components are continuous) th — Hg = Ks (tangential components are related by the linear current density Ks — assuming the current ﬂowing induces a magnetic ﬁeld in the direction of HQ) 7) Relation between magnetic ﬂux density B and magnetic ﬁeld H in any material. B = pH 8) Permeability u = mp0 (H/m) where u, - relative permeability of the material (no units) no - permeability of free space (air) = 47: * 10'7 (H/m) 9) Current Density] 2 I /A = 0' E (where 0‘ is the conductivity) 10) Current I = anv where q - Charge per particle n — Number of charged particles per unit volume A — Area through which the charge is moving V — Average velocity of each particle ...
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## This note was uploaded on 03/29/2008 for the course ECE 220 taught by Professor Hitchon during the Spring '05 term at Wisconsin.

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quiz5-solutions - ECE 220 — Quiz 5 (04/12/04) Please...

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