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SIMULATION OF ELECTROMAGNETIC FIELDS

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:
1

SIÓULATION OŃ

NLNCTROÓAGNNTIC

ŃINLMS

2

CONTENTS

1. MATLAB FOR BEGINNERS

1.1 Getting SWarWeT

1.2 Addition operation in MATLAB

1.3 Subtraction Operation

1.4 Multiplication OperaWion

1.5 Writing a program in MATLAB

1.6 General programming Commands in MATLAB

2.1 quiver3

2.2 vecWarrow

2.3 UolT

2.4 num2VWr

2.5 VqrW

2.6 WexW

2.7.1 xlabel

2.7.2 ylabel

2.7.3 Ylabel

2.7.4 WiWle

2.8 paWcU

2.9 Vurf

3. Co-OrTinaWe SyVWemV

3.1 Addition of two vectors using Parallelogram rule

3.2 ATTiWion of Wwo vecWorV uVing UeaT Wo Wail rule

3.3 PloWWing of uniW vecWorV

3.4 CalculaWion anT repreVenWaWion of uniW vecWor

3.5 IlluVWraWion of poViWion vecWor

3.6 PloWWing of poViWion vecWorV

3.7 CalculaWion of angle beWween vecWorV

3.9 RepreVenWaWion of planeV in X-Y anT R co-orTinaWeV

3.10 RepreVenWaWion of TifferenWial elemenW in CarWeVian co-orTinaWeV

3.11 RepreVenWaWion of Vurface RLPO Ǘ ŃRQVPMQP

3.12 RepreVenWaWion of Vurface wiWU Y conVWanW

3B13 5HSUHVHQPMPLRQ RI VXUIMŃH RLPO ǒ ŃRQVPMQP

3.14 RepreVenWaWion of VurfaceV in cylinTrical co-orTinaWeV

3.15 RepreVenWaWion of TifferenWial elemenWV in cylinTrical co-orTinaWeV

3.16 5HSUHVHQPMPLRQ RI VXUIMŃH RLPO lj ŃRQVPMQP

3.17 RepreVenWaWion of Vurface wiWU r conVWanW

3.18 5HSUHVHQPMPLRQ RI VXUIMŃHV RLPO U lj MQG Ǘ ŃRQVPMQP

3.19 NvaluaWion of Vurface anT volume inWegralV of a cylinTer

3

4.1 UVe of meVUgriT commanT

4.2 UVe of PeakV CommanT

4.4 Mivergnce

4.5 ConWour

4.6 NvaluaWion of Tivergence of a vecWor

4.7 CalculaWe anT ploW WUe Tivergence of a vecWor fielT

4.8 CalculaWe anT ploW WUe graTienW of a funcWion

4.9 PloW WUe graTienW of a funcWion

4.10 PloW WUe curl of a funcWion

4

1.1 GeWWing SWarWeT

b. When MATLAB® is iniWialiYeT; WUe TeVkWop appearV in iWV TefaulW layouW.

The desktop includes these panels:

CurrenW ŃolTer ³ AcceVV your fileV.

CommanT PinTow ³ NnWer commanTV aW WUe commanT lineH inTicaWeT PorkVpace ³ Nxplore TaWa WUaW you creaWe or imporW from fileV.

Editor Window

Command Window Workspace

Current

Folder

5 work Vpace aV maWrix .IWV ViYe can be founT by uVing WUe commanT size(a).

T. Columns are separated by commas or by space.

e. Rows are separated by semicolon. 6

Example 1:

7

Example 2:

1.3 Subtraction Operation

8

Example 1

1.4 Multiplication Operation

9

1.5 Writing a program in MATLAB

a) Click the New Script in the home tab b) Editor window opens as below 10 c) Write the program in this window

NxampleJ

Program Wo finT WUe Vum of 1 Wo n numberV

clc Jclc clearV WUe commanT winTow anT UomeV WUe curVor. 11 clear : Clear variables and functions from memory. Clear removes all variables from WUe workVpace. input JinpuW PrompW for uVer inpuW. Disp J MiVplay array. TiVp(X) TiVplayV WUe arrayH wiWUouW prinWing WUe array name

Save anT Run:

Saving the file:

For Executing the program click on the run command and a dialogue box will appear. CUange ŃolTer or ATT Wo paWU opWion can be cUoVen. 12 If there are no errors in the program MATLAB waits for the input AfWer enWering inpuW ouWpuW of WUe program will be TiVplayeT 13

Ńor

Ńor J Repeat statements a specific number of times. for O = 1JÓ for M = 1JÓ enT enT Ńig. 1.19 NxecuWion of for loop in commanT winTow

OuWpuW of WUe above inVWrucWionJ

14 Ńig. 1.19 NxecuWion of for loop in commanT winTow 15

IŃJ

if ConTiWionally execuWe VWaWemenWV.

TUe general form of WUe if VWaWemenW iV

if expreVVion

VWaWemenWV

NLSNIŃ expreVVion

VWaWemenWV

NLSN

VWaWemenWV

NNM Ńig. 1.19 NxecuWion of if VWaWemenW in commanT winTow 16 WHILE TUe while loop repeaWeTly execuWeV program statement(s) as long as the expression remainV Wrue.

TUe general form of a wUile VWaWemenW iVJ

while expreVVion

VWaWemenWV

enT a=10; wUile (aK20) a=a+1 enT

OuWpuWJ

a=11 a=12 a=13 a=14 a=15 a=16 a=17 a=18 a=19 a=20 17

2.1 quiver3

quiver3(XHYHRHUHVHPHS) plots velociWy vecWorV aV arrowV wiWU componenWV (uHvHw) aW WUe poinWV (xHyHY). TUe maWriceV XHYHRHUHVHP muVW all be WUe Vame ViYe anT conWain WUe correVponTing poViWion anT velociWy componenWV. IW auWomaWically VcaleV WUe arrowV Wo fiW anT WUen VWreWcUeV WUem by S. UVe S=0 Wo ploW WUe arrowV wiWUouW WUe auWomaWic

Vcaling. [ÓaWUworkV MocumenWaWion]

Nxample 2.1J

quiver3([0 0 0],[0 0 0],[0 0 0],[15 0 0],[0 15 0],[0 0 15]H0); IW ploWV vecWorV of lengWU equal Wo 15 in xHyHY planeV from origin. 18

2.2 vecWarrow

vecWarrow(p0Hp1) ploWV a line vecWor wiWU arrow poinWing from poinW p0 Wo poinW p1. TUe funcWion can ploW boWU 2M anT 3M vecWor wiWU arrow TepenTing on WUe TimenVion of WUe inpuW. [ÓaWUworkV MocumenWaWion]

Example 2.2

p0 = [1 2 5]; % CoorTinaWe of WUe firVW poinW p0 p1 = [2 5 6]; % CoorTinaWe of WUe VeconT poinW p1 vecWarrow(p0Hp1); Ńig 2.2 PloW inTicaWing arrow connecWing poinWV p0 anT p1 19

2.3 UolT

UolT ON UolTV WUe currenW ploW anT all axiV properWieVH incluTing WUe currenW color anT lineVWyleH Vo WUaW VubVequenW grapUing commanTV aTT Wo WUe exiVWing grapU wiWUouW reVeWWing WUe color anT lineVWyle. hold OFF reWurnV Wo WUe TefaulW moTe wUereby PLOT commanTV eraVe WUe previouV ploWV anT reVeW all axiV properWieV before Trawing new ploWV. hold, by itself, toggles the hold state. [ÓaWUworkV MocumenWaWion]

Example 2.3

p0 = [1 2 5]; % CoorTinaWe of WUe firVW poinW p0 p1 = [2 5 6]; % CoorTinaWe of WUe VeconT poinW p1 p2 = [3 6 7]; % CoorTinaWe of WUe VeconT poinW p2 vecWarrow(p0Hp1);

UolT on;

vecWarrow(p0Hp2); Ńig 2.3 PloW inTicaWing arrowV connecWing poinWV p0 anT p1 F p0 anT p2H obWaineT uVing UolT commanT 20

2.4 num2VWr

num2VWr ConverW numberV Wo cUaracWer repreVenWaWion T = num2VWr(X) converWV WUe maWrix X inWo iWV cUaracWer repreVenWaWion T wiWU abouW 4 TigiWV anT an exponenW if requireT. TUiV iV uVeful for labeling ploWV wiWU WUe TITLNH

Example 2.4

quotesdbs_dbs4.pdfusesText_7
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