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Unformatted text preview: ECE 3025: Electromagnetics
School of Electrical and Computer Engineering Georgia Institute of Technology
Professor Wﬂliam D. Hunt Exam #2 Name: Kc
November 1, 2005 Prof. William D. Hunt Total # of Points: 133pts This test is CLOSED BOOKa closed notes, no calculator but you are allowed to have the front
and back of two 3"X5" index cards. Show your work Where appropriate. Short Answer:
l.(5 pts) The Continuity equation relates
a. A charge distribution to the induced magnetic ﬁeld.
Kb) Time derivative of the volume charge density to the divergence of the current
density.
c. A current distribution to the induced magnetic ﬁeld.
d. Divergence of the current density to the integral over time of the volume charge
density
2.(5 pts) Laplace’s equation applies:
When there is volume charge present
Ll} When there is no volume charge present
c. When there is a high frequency magnetic field.
(1. None of the above.
3 (5 pt“) Calculation of the capacitance of a structure requires:
a. Knowledge of the charge distribution in the structure.
b. Knowledge of the current distribution in the structure.
,9“ Knowledge of the variation of the potential in the structure.
W a and c
e. b and c
4.(5 p.s)'\ The Hall effect:
Is a manifestation of the force on current in the presence of a magnetic ﬁeld.
b. Is a manifestation of the force on current in the presence of an electric ﬁeld.
C. Is commonly used to analyze various types of magnetic materials.
d. a and c
e. b and c 5.(lO pts) Write the differential form of Ampere’s Law. Write the boundary condition which
results from this law and explain What each of the components are (e. g direction: of the normal vector). ‘4
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be emf“; ) = K “7 {a} A K 6 Va ' 0“”‘11" Q O‘K_(9 Z l’ 2 "*
1;: gland/C diff!!! in. “r ere—u e
6. (3 Opts) Assume the quasistatic case. Sketch each case and expieefs the boundary conditions for the following in the most detailed, simpliﬁed form. Give an expression for the surface normal. For examnle if the Situahen calls for mannetm "01d .szvlulnlgwn. I: , 8 yaw 13w. boundary conditions, then include only the magnetic ﬁeld boundary conditions. (I
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(’W‘ J é a. A uniform dielectric sphere (E1) immersed in a conducting ﬂuid, like mercury.
An electric ﬁeld is applied. b. An inﬁnitely long conductive cylinder in air. The conductor is carrying current. c. A conductive inﬁnite cone of angle (1 lies over an inﬁnite ground plane. A
voltage, V, is applied between the cone and the ground plane. The medium
between the cone and the gromd plane is glass. 1 i . icon/I
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m 1:: ' 1* tie; J I Problems: Show your work. You will receive littie or at: credit if you simply write down
an answer«even if that answer happens to be correct. You will receive far more partial
credit by showing your work, even if you come up with the wrong answer. 7. Consider two perfectly perfectly conducting spheres with a dieieetrie medium of
permittivity 6. between them. The inner sphere is of radius a and the outer sphere is of radius b. A voltage V0, is applied to the inner sphere with the outer sphere grounded. a. (6 pts)Sketch the conﬁguration. What coordinate system should be used? b. (8 pts)Begin with the appropriate fonn of Laplaee’s equation and simplify as
much as possible. 0. (12 points)Solve fer the potential between the two spheres. You cannot have any
mmnown coefﬁcients in your solution. (V o is known.) (1. (10 pts)Find the charge density, pg, on the surface of the outer sphere. e. «(15 point bonus question) Find the eapacitance of this/“structure. jun/:1 roarifhe‘liieu a: 9" a p ‘ gay
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l ’ ~= .7 + {J "' 1A (Lt. si.) me ., R)
V ISLka 3"? VK: 8. Consider coaxial cable which contains two coaxial conductors. Assume the inner
conductor is solid and of radius a and carries a current of I. The outer conductor is also solid and
begins at radius 1) and ends at radius c and carries a current of ~1 . We have a < b < c. For the
purposes of this problem, assume that the ﬁeld does not go to zero inside the conductors. (5 pts) Sketch the problem and deﬁne the coordinate system and axis directions. (8 pts)F ind the magnetic ﬁeld, H, inside the inner conductor. (8 13$)?in the magnetic ﬁeld, H, between "the cylinders. (8 pts)Find the magnetic ﬁeld, H, inside/within the outer conductor. (8 pts)Find the magnetic ﬁeld, H, outside the outer conductor. If 9‘s .099 1' l?
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