Schaum’s outline of theory and problems (6)

➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạm

Loại tài liệu: PDF

Số trang: 343 Trang

Tài liệu: ✅ ĐÃ ĐƯỢC PHÊ DUYỆT

TẢI VỀ

Nội dung chi tiết: Schaum’s outline of theory and problems (6)

Schaum’s outline of theory and problems (6)

ELECTROMAGNETICSCHAP. 1|VECTOR ANALYSISEXAMPLE 1 Given A = 2a, + 4a, - 3a, and •find A • B and A X B.A • B = (2XD + (4X-1) + (-3)10)- -2AXB-a, 21A 4 -

Schaum’s outline of theory and problems (6) -1■-3a, “3a,-6a,14 COORDINATE SYSTEMSA problem which has cylindrical or spherical symmetry could be expressed and solved in the familiar cartesian coo

rdinate system. However, the solution would fail to show the symmetry and in most cases would be needlessly complex, 'l"hercforc, throughout this book Schaum’s outline of theory and problems (6)

, in addition to the cartesian coordinate system, the circular cylindrical and the spherical coordinate systems will be need All three will he examine

Schaum’s outline of theory and problems (6)

d together in order to illustrate the similarities and the differencesA point p is described by three coordinates, in cartesian (x, y, z), in circular

ELECTROMAGNETICSCHAP. 1|VECTOR ANALYSISEXAMPLE 1 Given A = 2a, + 4a, - 3a, and •find A • B and A X B.A • B = (2XD + (4X-1) + (-3)10)- -2AXB-a, 21A 4 -

Schaum’s outline of theory and problems (6) y followed. The angle Ộ is the same angle in both the cylindrical and spherical systems. But, in the order of the coordinates, Ộ appears in the second

position in cylindrical, (r, Schaum’s outline of theory and problems (6)

for two quite different things In cylindrical coordinates r measures Che distance from the z axis in a plane normal to the z axis, while in the spheri

Schaum’s outline of theory and problems (6)

cal system r measures the distance from the origin to the point. It should be dear from the context of the problem which r ic intendedA point is also

ELECTROMAGNETICSCHAP. 1|VECTOR ANALYSISEXAMPLE 1 Given A = 2a, + 4a, - 3a, and •find A • B and A X B.A • B = (2XD + (4X-1) + (-3)10)- -2AXB-a, 21A 4 -

Schaum’s outline of theory and problems (6) t., y-const., and z« const. In cylindrical coordinates, z -const, is the same infinite plane ax in cartesian; ự> -const, is a half plane with its edge

along the z axis; r - const, is a right circular cylinder. These three surfaces are orthogonal and their intersection locales point p. In spherical c Schaum’s outline of theory and problems (6)

oordinates, Ộ ■ const, is the same half plane as in cylindrical; r —const. is a sphere with its center at the origin; Ơ-const, is a right circular con

Schaum’s outline of theory and problems (6)

e whose axis IS the z axis and whose vertex is at the origin. Note that 0 is limited to the range Os Ỡ Sx,figure 1-4 slivwa the three unit »cdvn at pv

ELECTROMAGNETICSCHAP. 1|VECTOR ANALYSISEXAMPLE 1 Given A = 2a, + 4a, - 3a, and •find A • B and A X B.A • B = (2XD + (4X-1) + (-3)10)- -2AXB-a, 21A 4 -

Schaum’s outline of theory and problems (6) (except in the case of af). Each unit vector is normal to its coordinate surface and is in the direction in which the coordinate increases. Notice tha

t all these systems are right-handed:•, X Ba = ■»CHAP. 6|CURRENT, CURRENT DENSITY. AND CONDUCTOR.6.43.In cylindrical coordinates. J ■ lOr (A/m2) (or ( Schaum’s outline of theory and problems (6)

he region 0.01 Sr < 0.02 m. 0 — coneX.Anj. 2.33x10’* A6.44.Giv

Schaum’s outline of theory and problems (6)

en a current densityJ-(A/m*)in spherical i-wtdinalcs. find the current crossing the cvntcol strip Ỡ - rt/4. 0.001 = r = 0.080III. Ans. 1.38x10* A6.44.

ELECTROMAGNETICSCHAP. 1|VECTOR ANALYSISEXAMPLE 1 Given A = 2a, + 4a, - 3a, and •find A • B and A X B.A • B = (2XD + (4X-1) + (-3)10)- -2AXB-a, 21A 4 -

Schaum’s outline of theory and problems (6) y \ + 2xya, (A/m*). Am. 3.0 A6.46.As shown tn Fig. 6-IV, a current of 50 A passes down the I axis, enters a thin spherical shell ot radius 0.03m. and

at 8 = jr/2 enters a plane sheet. Write expression* for the current sheet densities K in the spherical shell and in the plane.JSuL2657 96Ans. (A A"). Schaum’s outline of theory and problems (6)

(A/nt)sin ifr6.47.A filamentary current of /(A) passes down the I axis to z■ 5X 10 ’in where it enters the portion OíộSx/4 of a spherical shell of rad

Schaum’s outline of theory and problems (6)

ius 5 X 10 *111. Find K for this current sheet.80/*"

ELECTROMAGNETICSCHAP. 1|VECTOR ANALYSISEXAMPLE 1 Given A = 2a, + 4a, - 3a, and •find A • B and A X B.A • B = (2XD + (4X-1) + (-3)10)- -2AXB-a, 21A 4 -

Schaum’s outline of theory and problems (6) ne, (b) Find the current crossing the square u I-0.25 111. |y|s0.25ni. 2=0. Am. (o) 27.9 A; (ft) 12.5 A6.49.A Im41ow. thin-wallcd. levtangular conduct

or 0.01 by 0.02 in carries a current Schaum’s outline of theory and problems (6)

X +y -3m and extends toward the origin. At the surface the electric held intensity ts 0JS v/m. Express E and D at the surface and find 0,.Ans. ±a247(

Schaum’s outline of theory and problems (6)

a. I ■>) v/m, 12.19 X to •*(•.+•,) C/m2. xiiox631.A conductor that extends into the region I <■ 0 has one face in the plane 2=0. over wlikti tlierc B

ELECTROMAGNETICSCHAP. 1|VECTOR ANALYSISEXAMPLE 1 Given A = 2a, + 4a, - 3a, and •find A • B and A X B.A • B = (2XD + (4X-1) + (-3)10)- -2AXB-a, 21A 4 -