Final 2024
.pdf
School
Dalhousie University**We aren't endorsed by this school
Course
ECED 3300
Subject
Physics
Date
Dec 19, 2024
Pages
3
Uploaded by DoctorKnowledge26781
ECED 3300Electromagnetic FieldsFinal ExaminationPlace:D406Instructor:Sergey A. PonomarenkoDate and Time:Saturday, December 14, 2024, 3:30 to 6:30 pm.Open Books:no electronic devices are allowed.Hint:Make sure to justify all your answers to get full credit.1
Problem 1 (20pts)Find an attraction force between the plates of a very long cylindrical capacitor of lengthlandinner and outer radiiaandb, respectively, if the capacitor plates carry charges±Q. The materialin between the plates is a dielectric of permittivity .Problem 2 (20pts)The vector potential in a region of free space is given by the expressionA=β2(yez-zey), z >0;β2(zex-xez), z <0,whereβis a known constant.1. (10 pts) Determine the magnetic flux density everywhere in the region.2. (10 pts) What is the surface current density, if any, at the interfacez= 0?Problem 3 (25pts)A very long, straight solid cylindrical conductor of radiusbcarries a current along its axis. Thecurrent isnonumiformlydistributed over its cross-section with the densityJ(ρ) =2Iρ2πb4ez, whereIis known. A coplanar square conducting loop of sizeais located a distancedaway from thecenter of the conductor as is shown in the figure below.1. (10 pts) Determine the mutual inductance between the loop and the conductor.2. (15 pts) What is the self-inductance of the solid conductor per unit length?FIG. 1: Illustrating geometry of Problem 3.2
Problem 4 (30pts)A point dipole with the dipole momentpis placed at the apex of a cone of heightHand angleα.The dipole points along the axis of the cone as is shown in the figure below.1. (10 pts) Find the electric field at any point on the rim of the base of the cone, shown in red.2. (5 pts ) Find the work required to have a point chargeqmake a complete turn around the rim.3. (15 pts) How much work is necessary to transport a test dipolep0, pointing in the radial directionaway from the center of the rim, along the arc subtending the angleβon the rim and rotating thedipole such that it is aligned withp? The initial and final positions and directions of the test dipoleare shown in the figure.FIG. 2: Illustrating geometry of Problem 4.Problem 5 (40pts)Three infinitely long wires, carrying identical filamentary currentsI, are placed along the threemutually orthogonal coordinate axes as is indicated in Fig.3 below.1. (35 pts) Find the magnetic field due to the wires at any point in spacenotlocated on either wire.2. (5 pts) Where does the field vanish, if at all?FIG. 3: Illustrating geometry of Problem 5.3