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# EMT Assignment 2

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ELECTROMAGNETIC FIELD THEORY
ASSIGNMENT-II
3rd SEMESTER, E&E ENGINEERING, MIT-MANIPAL
SUBMISSION DATE: 19/11/2011
---------------------------------------------------------------------------------------------------------------------------
1. Let Vm = (2x2 + 4x - 2y2) in a certain region of free space. Find the vector force exerted
on a straight wire segment in this region if it extends from origin to: (a) PA (1, 0, 0) and
carries 5A in the ax direction; (b) PB (0, 0, 1) and carries 5A in the az direction; (c) PC (0.6,
0.8, 0) and carries 5A away from the origin.

2. The magnetic flux density in a region of free space is given as B = (-3x ax + 5y ay - 2z az)
T. Find the total force on the rectangular loop as shown in figure Q2 if it lies in the plane
z = 0 and is bounded by x =1, x=3, y=2 and y=5 , all dimensions are in cm.

3. A very long, straight wire carries a current of 500A. An 80cm x 20cm rectangular loop
carries a current of 20A. If the 80cm side of the loop is parallel to the wire as shown in
figure Q3, evaluate the magnetic force acting on the loop.

4. A unit normal vector from region 2 ( = 20) to region 1 ( = 0) is an21 = (6ax + 2ay -
3az)/7. If H1 = (10ax + ay + 12az )A/m and H2 = (H2x ax - 5ay + 4 az) A/m, determine
a) H2x
b) The surface current density K on the interface
c) The angles B1 and B2 make with the normal to the interface.

5. The square loop of wire has corners at (0,0,0) , (0.2, 0,0), (0.2,0.2,0) and (0,0.2,0) at t=0.
The loop is perfectly conducting except for a small 100 resistance on one side. It is
moving through the field B = 5 cos (6 x 108 t - 2x) az T with a constant velocity of 40 ay
m/s. Calculate the average power being delivered to the resistor as a function of time.

6. Given the magnetic flux density B = 6 cos 106t sin 0.01x az mT, find the value of the
closed line integral of E around the perimeter of the surface z =0, 0<x<20m, 0<y<3m at t
= 1s.

7. The parallel plate transmission line shown in figure Q7 has dimensions b= 4cm and d=
8mm, while the medium between the plates is characterised by r =1, r = 20, and =
0.Neglect the fields outside the dielectric. Given the field H = 5 cos (109t - z) ay A/m, use
Maxwell's equations to find: (a) , if >0; (b) the displacement current density at z = 0;
(c) the total displacement current crossing the surface x = 0.5d, 0<y<b, 0<z<0.1m in the
ax direction.

8. The magnetic field component of a plane wave in a lossless dielectric (r = 1) is H = 30 sin
(2 x 108t - 5x) az mA/m . Find (a) r ; (b)wavelength and wave velocity; (c) polarisation
of the wave ; (d) corresponding E component; (e) intrinsic impedance; (f) displacement
current density.

9. In a non-magnetic material, H = 30 cos (2 x 108t -6x) ay mA/m , find :(a) intrinsic
impedance, (b) the Poynting vector, (c) the time-average power crossing the surface x
=1, 0 < y <2, 0 < z < 3m.

10. A uniform plane wave in air with E = (10 ay + 5 az) cos (t + 2y -4z) V/m is incident on a
dielectric medium (z 0) having = 0, = 40, = 0. Calculate
a) The angles of incidence, reflection and transmission
b) The reflection and transmission coefficients
c) Total E in free space
d) Total E in the dielectric the Brewster angle
Fig: Q2

Fig: Q3

Fig: Q7
1. (a)0 N; (b)-25.133 ay N; (c)32.170 az N
2. -36 az mN

3. ;
4. (a) 5.833; (b) 4.86ax -8.64ay + 3.95az A/m ;(c) 76.27 , 77.62
5. ;
6. 30.192 kV
7. (a) = 14.9 rad/m; (b) -74.5 sin(109t)ax A/m; (c) 0.20[ cos(109t - 1.49) - cos(109t)] A
8. ;
9. ;
10. ;

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