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National Institute of Technology

Rourkela

Assignment No.-1

Subject: Electromagnetic Theory

o!e :

Issue "ate:

#ages :6"ea! $ine:

To%ic: &ector Analysis 'aculty:#rof. Subrata (aiti

)ranch *Sem+:

EE *,th+

SETIN-A #roblems base! on ylin!rical an! S%herical oor!inates/

0.,

0.

0.12

Express the following vectors in rectangular coordinates.

(a) A=sina+ cos a+2z az

(b) B=4 r cos a

r

+r a

0.1

Given thatA=3 a+2a+az and

5a8az , find:

(a) A+

(b)A.

(c) A!

(d)"he angle between A and

0.13

#

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0.01

0.04

0.05

$et

4+2cos a3z az

2zsina+A=

and

B= cosa+sin a+az .

(a) %ind the &ini&u& angle between Aand )at (#, 6'', #).

(b)eter&ine a unit vector nor&al to both Aand )at (#, *'', ').

SETIN-) #roblems base! on "ifferential $ength6 Area6 an! &olume/

4.0

sing the differential length dl , find the length of the following curves:

r=4,300

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y=1,0

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4.42 2erif3 the divergence theore& for the function

SETIN-' #roblems base! on url of a &ector an! Stoke;s Theorem/

4.4,

4.54%ind the divergence and curl of

(a) B= cosa+2sin a4z az

(b) F=r2sinar+2 rcos a

SETIN-9 #roblems base! on $a%lacian of a Scalar/

4

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4.53

4.75

5how that A=xz ax+z2ay+yz az satisfies the following vector identit3.

( A )= ( . A )2A .

SETIN-< #roblems base! on lassification of &ector 'iel!s/4.77

0onsider the following vector fields:A=x ax+yay+z az

B=2cos a4 sina+3az

C=sinar+r sina

hich of these fields are (a) solenoidal, and (b) irrotational7

4.7,Given the vector field

G=(16xyz )ax+8x2ayx az

(a) 8s9 irrotational (or conservative)

(b) %ind the net flux of 9 over the cube 0