# SJSU EE 140 - soln140_MT1B_S15 (1) (4 pages)

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## soln140_MT1B_S15 (1)

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- Pages:
- 4
- School:
- San Jose State University
- Course:
- Ee 140 - Principles of Electromagnetic Fields

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EE 140 Spring 2015 Mid Term 1 Dr Ray Kwok Name Last First 1 In radio frequency current practically flow ONLY on the surface of a conductor Consider a coaxial cable with a inner conductor of radius a and a grounded metal shield of inner radius b and outer radius c as shown Total current in the inner conductor is I Plot B field as a function of r What is the surface current density at r a At r b And at r c c b a r r B d l o I enclosed J r a 0 B B r a 0 a r b B oI 2 a B o I 2 b B 2 r o I B o I 2 r B r b 0 conductor B r c 0 Net I 0 r J s r a I 2 a I J s r b 2 b J s r c 0 a b c EE 140 Spring 2015 Mid Term 1 Dr Ray Kwok 2 a A ring of charge with linear charge density and radius R is lying on the xy plane Find the electric potential at a distance z above the center of the ring b Take the gradient of this V to find the electric field at that point 0 0 z c Apply the electric potential from part a to a 2 dimensional disk Find the electric potential of a charged disk with surface charge density radius R at a distance z above the center of the disk kdq k Rd r r k R 2 R V r 2 o R 2 z 2 dV r R z r V Rz E z z 2 o R 2 z 2 3 2 z Q 2 r 2 rdr dV V dr r 2 o r 2 z 2 2 o R 0 rdr 2 r z 2 u 1 2 du 2u1 2 4 o 4 o 2 o r 2 z2 2 R z z R 2 0 o 2 EE 140 Spring 2015 Mid Term 1 3 A conducting rod with length L moves in a magnetic field B directed into the plane of the figure The rod moves with a speed v in the direction shown a What is the potential difference between the ends of the rod b Which side has higher potential c When the charges in the rod are in equilibrium what are the magnitude and direction of the electric field within the rod Dr Ray Kwok v x x x x x x x x x x x x x x x x x x x x x x x x x x x x r r r F qv B qvB r L F r VL Vo dx vBL q 0 Positive charges move to the right So the right side would end up with more charges and hence higher V potential VL Vo r r r qE qv B r E vB x x x x x x x x x x x x x x B EE 140 Spring 2015 Mid Term 1 Dr Ray Kwok 4 What is the B field of an infinite wire carrying a current I at a distance d away Use this result to find the B field of an infinite current sheet A simple model is this Infinitely long straight conductors with square cross sections and each carrying current I are laid side byside to form an infinite current sheet as shown in figure The conductors lie in the xy plane are parallel to the y axis and carry current in the y direction There are n conductors per unit length along the x axis What are the magnitude and direction of the magnetic field a distance z above the current sheet r r B d l o I enclosed B 2 d o I B o I 2 d x I ndx I ndx I dB o 2 r z dB r I dB x dB cos x y o ndx I z 2 r r r o nIz dx B x 2 r 2 x z tan dx z sec 2 d r z sec 2 dx z sec 2 d 1 r 2 z sec 2 z d2 z r nI B x o 2

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