magnetic field tutorials

1. Kathmandu Engineering College Kalimati, Kathmandu
Department of Electronics and Computer
Tutorial No - 5
1) The magnetic flux density may be represented by Bz = sin 1000t mWb/m2
for
ρ<0.2 m (a) Find the magnetic flux passing through the surface ρ0.1, z= 0, in the az
direction. (b) Find E at ρ = 0.1, = /4, z = 0.
Ans:- (a)21.8 sin1000z µWb (b) -108.9cos 1000t mV/m.
2) Find the displacement current density: (a) next to your radio, in air where the local FM
provides a carrier having H = 0.2cos [2.10(3x108
t – x)] az A/m (b) in the air space within a
large power distribution transformer with B = 1.1 cos[1.257 x 10-6
(3x108
t –y)] ax Wb?m2
(c) Inside a large oil filled power capacitor where ЄR = 6 and E = 100 cos [1.257 x 10-6
(3x108
t -2.45 Z )] ay KV/m (d) In a typical metallic conductor at 60Hz where  = 5x107
mho/meter,
Є=Є0 and J =106
sin[117.1(3.22t –z) ] ax A/m2
Ans:-(a) -0.42sin[2.10(3x108
t – x)] ay A/m2
(b) -1.1 sin[1.257 x 10-6
(3x108
t – y)] az A/m2
(c) 2.002 cos[1.257 x 10-6
(3x108
t – 2.45 z )] az A/m2
(d) 66.74 cos[117.1(3.22 t – z)] ax
PA/m2
3) Find the displacement current density: (a) next to your radio, in air where the local FM
provides a carrier having H = 0.2cos [2.10(3x108
t – x)] az A/m (b) Inside a large oil filled
power capacitor where ЄR = 6 and E = 100 sin[1.257 x 10-6
(3x108
t -2.45z )] ax KV/m (c) In
a typical metallic conductor at 60Hz where  = 5x107
mho/meter, Є=Є0 and J =106
sin[117.1(3.22t –z) ] ax A/m2
4) The electric field intensity of a uniform plane wave in air has amplitude of 800 V/m and is in
the ax direction. If the wave is propagating in the az direction and has the wavelength of 2 ft
find (a) the frequency (b) the period (c) the value of K if the filed is expressed in the form A
cos( t – kz) (d) the amplitude of H.
Ans:- (a) 492 MHz (b) 203ns (c) 10.31 rad/m (d) 2.12A/m
5) If Hs = [5ej20
) ax – (3+j1) ay] e-jkz
A/m in free space and f = 6MHz , find the instantaneous
magnitude of H at (a) (0,0,0) at t= 0; (b) (0,0,0) at t =0.1µs; (c) (2,5,8) at t =0; (d) (2,5,8) at t
=0.1µs
Ans:- (a) 5.57 A/m (b) 3.35 A/m (c) 4.66 A/m (d) 5.91 A/m
6) Find the value of K given in µ so that given pair of fields of E = 60 sin 106
t sin0.01z ax V/m
and H = 0.6 cos 106
t cos 0.001z ay A/m satisfy Maxwell’s equations for time varying case
Assume that  = 0 ,ρV = 0 and µ = k.
Ans:-
7) Select the value of K so that each of the following pairs of fields satisfies Maxwell’s
equations in a region where  = 0 and ρV = 0. (a) E = (Kx – 100t) ay V/m; H = (x + 20t) az
A/m if µ= 0.25 H/m and Є = 0.01 F/m (b) D = 5x ax – 2y ay+ Kz az µC/m2
; B = 2 ay MT if
µ = µ0 and Є=Є0
a) -5 b) -3
8) Given H

= âθ+54rcosθâϕ and region θ=20͘, 0≤ϕ≤2, 0≤r≤5, find the current in âθ
direction for the given region. Verify stokes’ theorem for the given direction
Ans:- -2.73x103
A
9) A filamentary current of infinite extent has current of 10A flowing along z-axis. Find
magnetic field intensity H at point P (0, 2, 0).
10) A current filament carrying 15A in the âz direction lies along the entire z-axis. Find H

in
rectangular coordinates at; (a) PA (20, 0, 4); (b) PB (2,-4, 4).
Ans:- (a) 0.54ây A/m (b) 0.477âx + 0.239ây A/m

2. Kathmandu Engineering College Kalimati, Kathmandu
Department of Electronics and Computer
11) Medium one and medium two are separated by z-0 plane. Medium one (z>0) has μr1=2 and
medium two (z<0) has μr2=3. If plane z=0 carries no current and B2=2âx+3âz in medium two
then find B1 in medium one.
12) Find the magnetization M for the region where μr=5 and H= âx+ây+âz.
Ans:- 4âx+4ây+4âz A/m
13) The magnetic Flux density in a magnetic material with m = 6 is given in a certain region as
B

= 0.005y2
âx T at y=0.4m, find the magnitude of J

Ans:- -454.959 aˆ z A/m2
14) Given a magnetic flux density, B

=6Cos106
tSin0.1âz μT find the:
i. Magnetic flux passing through the surface z=0 ,0<x<20, 0<y<3m at t=1μs;
ii) Total Emf generated around the perimeter of the above surface at t=1μs
Ans:i) 0.3588cos106
t ii) 30.192KV
15) Express the value of H in cartesion components at P(0,0.2,0) in the field of a current
filament, 2.5 A in âz direction at x=0.1,y=0.3.
Ans:- -1.989âx-1.989ây A/m
16) For a certain ferrite material which is operating on a linear mode with B= 0.05 T and
μr = 50, calculate the value for
(i) Magnetic Susceptibility m.
(ii) Magnetic Field intensity H
Ans:- i) 49 ii) 796.17 A/m
17) A circular loop located on x2
+ y2
= 9, z = 0 carries a direct current of 10A along aˆ .
Determine H at ( 0, 0, 4) and ( 0, 0, -4) .
Ans:- 0.36âz A/m; 0.36âz A/m
18) A parallel plate capacitor with plate area of 5cm2 and plate separation of 3mm has a voltage
50sin103t V applied to its plates. Calculate the displacement current assuming =20
Ans: 147.4cos103
t nA
19)The conducting triangular loop in the figure shown below carries a current of 10A. Find H

at
(0,0,5) due to
i) side 1 of the loop.
ii) side 3 of the loop
Ans: i) -59.1ây mA/m ii) -30.63âx + 30.63ây mA/m
20) Evaluate both side of the stoke’s theorem for the field H

= xyâx – 3y3
ây A/m for the
rectangular path around the region 2x5;-1y1;z=0. Let the positive direction of dS be âz.
10A
2
3
1
1
2
X
y

3. Kathmandu Engineering College Kalimati, Kathmandu
Department of Electronics and Computer
Ans:- 126
21) Within a certain reason, =10-11
F/m and μ = 10-5
H /m. If B

x = 2x 10-4
cos 105
t sin 10-3
y T: (a)
use  x H

=  to find E

; (b) find the total magnetic flux passing through the surface x = 0, 0 <
y < 40 m, 0 < z < 2m, at t=1μS; (c) find the value of the closed line integral of E

around the
perimeter of the given surface.
Ans:- (a)-20000sin105
t cos10-3
y aˆ z V/m; (b) 0.318mWb; (c) 3.19 V