NEPAL ENGINEERING COLLEGE
Changunarayan, Bhaktapur
ELECTROMAGNETICS
Tutorial: I (Review)
Assigned Date: 11 March 2013
Submission date: 18 March 2013
Assume that the boldfaced letter represents vector and asubscript represents a unit vector.
1.) Let A= ax+2ay-3az , B = 0ax - 4ay +az , C= 5ax +0ay -2az. Find:
i)aA ii.)A.B iii.) Comp. of A in C iv.) A.(B X C) and (A X B).C v.) Angle between A and
B(өAB) vi.) (A X B) X C vii.) |A-B| viii.) A X (B X C).
2.) If A(2,5,-1), B(3,-2,4), C(-2,3,1) Find
i.)
Rab . Rac
ii.)
|Rab|, |Rac|
iii.)
The angle between Rab and Rac
iv.)
The length of the projection of Rab on Rac
v.)
The vector projection of Rab on Rac
3.) The vector Rab extend from A(1,2,3) to B. If the length of Rab is 10 units and its direction is
given by aAB = 0.6ax +0.64ay +0.48az, find co-ordinates of B.
4.) Vector A=3ax +4ay -5az and B=-6ax +2ay +4az extend out from the origin. Find
i.)
the angle between A and B
i.)
the distance between the tips of the vectors
ii.)
the unit vector normal to the plane containing A and B
iii.)
the area of the parallelogram of which A and B are adjacent sides
5.) The three vertices of a triangle are located at A(6,-1,2), B(-2,3,-4), C(-3,1,5). Find
i.)Rab X Rac ii.) The area of the triangle iii.) A unit vector perpendicular to the plane in which
the triangle is located.
6.) Given the two vectors, rA = -ax -3ay -4az and rB = 2ax +2ay +2az, and point C (1,3,4), find:
i.) RAB; ii.) a unit vector directed from C toward A.
7.) Given the vector field, F=0.4(y-2x)ax - [200/( x2 + y2 + z2 )]az: (a) evaluate | F | at P (-4,3,5) ; (b)
find a unit vector specifying the direction of F at P. Describe the locus of all points for which :
(c) Fx = 1; (d) | Fz | = 2.
Prepared By: Chandra Thapa
8.) Given P (ρ = 6, Φ = 1250 z = -3) and Q ( x = 3, y = -1, z = 4 ), find the distance from: (a) P to the
origin; (b) Q perpendicularly to the z-axis; (c) P to Q.
9.) Given P (r = 6, θ = 1100, Φ = 1250 ) and Q (x = 3, y = -1, z = 4), find the distance from: (a) Q to
the origin; (b) P to the y = 0 plane; (c) P to Q.
10.)
Transform each of the following vectors to spherical coordinates at the point specified: a)
5ax at B(r = 4, θ = 250, Ф = 1200); b) 5ax at A(x = 2, y = 3, z = -1); c) 4ax – 2ay - 4az at P(x = -2,
y= -3, z = 4).
11.)
a)Express aρ in spherical components and variables. b) express ar in cylindrical
components and variables
12.)
Given vector A = y ax + (x + z) ay in Cartesian co-ordinate system at point P(-2,6,3).
Convert the vector A with cylindrical & spherical co-ordinate.
Answer to Tutorial :-1
1) i.) (1/√14ax+2/√14ay-3/√14az) ii.) -11 iii.) 11/√29 iv.) -42 v.) 135.48˚ vi.) 2ax40ay+5az vii.) C53 viii) 55ax-44ay-11az
2) i.) 20 ii.) √75, √24 iii.) 61.87˚ iv.) 20/√24 v.) 5/6(-4ax-2ay+2az)
3) (7, 8.4, 7.8)
4) i.) 55.46˚ ii.) 12.884 iii.) 1/43.58(26ax+18ay+30az) iv.) 43.59
5) i.) 24ax+78ay+20az ii.) 42 iii.) 0.2ax + 0.928ay + 0.23az
6) i.) 3ax + 5ay + 6az ii.) -0.196ax -0.588ay - 0.784az
7) (a) 5.946 (b) 0.740ax – 0.673az (c) plane: y = 2x + 2.5; (d) sphere: x2 + y2 + z2 = 100
8) (a) 6.71; (b) 3.16; (c) 11.2.
9) (a) 5.10; (b) 4.62; (c) 10.35.
10) (a) -1.057ar -2.266 aθ -4.33 aФ (b) 2.673ar -0.741 aθ – 4.160 aФ (c) -3.343ar +2.266
aθ -4.438 aФ
11) (a) A = sinθar + cosθ aθ (b) (1/(ρ2+z2)1/2)(ρaρ + zaz)
12) P(-2, 6, 3) = P(6.032, 108.43, 3) = P(7, 64.62, 108.43)
A= 6ax+ ay
A= -0.9487aρ – 6.008a
A= -0.8571ar – 0.4066aθ – 6.008a
Prepared By: Chandra Thapa