EE140 Spring 2021 Mid Term 2 Dr Ray Kwok 1 y A ring made of thin wire is placed in a magnetic field 3 4 5 cos 60 Tesla The radius of the ring is oscillating as r 2 sin 0 5t meters Find the magnitude and direction of the induced current The resistivity of the wire is m o x r 5cos 60 2 300 sin 60 2 5 cos 60 2 300 sin 60 2 5 cos 60 0 5 For small t the dA dt term dominates changing area Lenz s Law increasing area more flux induced B is induced current is CCW at t 0 CCW 5 cos 60 0 5 300 sin 60 2 2 5 cos 60 0 5 150 sin 60 2 EE140 Spring 2021 Mid Term 2 Dr Ray Kwok 2 A LONG coaxial cable of radius a is carrying a non uniform current density 2 out of the page where is a constant The outer shield is a grounded conductor and a dielectric r is filled between the radii a and b The outer shield is grounded as shown a What is the magnetic B field inside the cable between radii a and b b Use the formula to derive the surface current density at r b c b a CCW Into the page sJHHn 212 4422 2 4422 2 44023402raBardrrIrBbrarBrrdrradJrBIdBarooaoinsideooorooinsideo 4 0 4 0 4 4 4433212pageofoutJbazbarbrJaararJHHnsss EE140 Spring 2021 Mid Term 2 Dr Ray Kwok 3 A large block of material with permeability 2 o is found to be tilted at an angle of 37 from vertical as shown in figure The magnetic field inside and outside of the block are given below Find the induced surface current density vector Note cos 37 o 4 5 sin 37 3 5 o o z n 37o 1 o 2 o 37o y zyxBzyxB 5 10 6 2 321 osoossoozyzyJzyxzyxzyJHHnJzyzyn 35 4 32 5 10 6 2 35 4 3 5 4 337cos 37sin 272122 xxzyxJooos 2912221 5130430 5127 EE140 Spring 2021 Mid Term 2 Dr Ray Kwok 4 A car top antenna can be modeled as a current element above an infinite ground plane Assuming the current is constant find the magnetic field at a point P away from the antenna as shown in the figure P x y z z r L R I o I cscsincsc tansin 4 sin 4 42222RrrRdRdzzzRrdzIBrIdzrrlIdBdLLooo 2222222 222222 4 4 cos4 cscsincsc4 sin 4 yxRLzRLzLzRLzRIBzzRzzRIRIRdRIrdzIBoLLzoooLLo
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