nitr assignment
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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