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Bài giảng Electromagnetic Fields – Prob - Chapter 2 - Trần Quang Việt

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Electromagnetic Fields – Prob – ch_2  
B = B0 [sin(ωt )ax − cos(ωt )ay ] (Wb / m2 )  
D2.5. Given :  
find the induced emf around each of the following close paths: (a) the  
rectangular path from (0,0,0) to (0,1,0) to (0,1,1) to (0,0,1); (b) the  
triangular path from (1,0,0) to (0,1,0) to (0,0,1) to (1,0,0); and (c) the  
rectangular path from (0,0,0) to (1,1,0) to (1,1,1) to (0,0,1) to (0,0,0).  
ωB  
Ans :( a )−ωB0 cos(ωt ) (V );(b )−  
0 cos(ωt −π / 4 ) (V )  
2
( c )− 2ωB0 cos(ωt +π / 4) (V )  
Trần Quang Việt – BMCS – Khoa Điện – ĐHBK Tp.HCM  
Electromagnetic Fields – Prob – ch_2  
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E = E0te−t az  
D2.8. For :  
in free space, find the displacement  
current crossing an area of 0.1m2 in the xy-plane from the –z-side to  
the +z-side for each of the following value of t: (a) t=0;  
(b )t =1/ 2 S;and (c) t=1 S  
Ans :( a ) 0.1ε0E0 (A);(b ) 0 ( A);(c ) -0.1e-1ε0E0( A)  
P2.18. A current density due to flow of charges is given by :  
J = −( xax + yay + z2 az )A/ m2  
Find the displacement current emanating from each of the following  
close surfaces : (a) the surface of the cubical box bounded by the  
plane x= 2, y= 2, and z= 2, and (b) the surface of the cyclindrical  
box bounded by the surface r=1, z=0, and z=2  
Trần Quang Việt – BMCS – Khoa Điện – ĐHBK Tp.HCM  
1
Electromagnetic Fields – Prob – ch_2  
P2.22. For each of the following charge distributions, find the  
displacement flux emanating from the surface enclosing the charge :  
2
( a )ρ( r,φ,z ) = ρ0e−r for r<1, 0<z<1 in cyclindrical coordinates;  
and (b) ρ(r,θ,φ)=(ρ0/r)sin2θ for r<1, 0<θ <π /2 in spherical coordinates  
BdS = 0  
P2.23. Using the property that  
, find the absolute value  
of the magnetic flux crossing that portion of the surface y=sinx  
ꢂ∫  
S
B = B0( yax − xay ) Wb / m2  
bounded by x=0, x=π, z=0 and z=1 for :  
P2.29. Charge is distributed with uniform density ρ0 C/m3 in the  
region a<r<2a in spherical coordinates. Find  
plot Dr versus r.  
everywhere and  
D
Trần Quang Việt – BMCS – Khoa Điện – ĐHBK Tp.HCM  
Electromagnetic Fields – Prob – ch_2  
2
P2.28. Charge is distributed with uniform density ρ0e−r C / m3 in  
the cyclindrical region r<1. Find everywhere.  
D
P2.31. Current flows with density  
A/m2 along an  
J = J0( r / a )az  
infinitely long solid cyclindrical wire of radius a having the z-axis  
as its axis. Find everywhere and plot Hφ versus r.  
H
P2.32. A coxial cable consits of an inner conductor of radius 3a and  
an outer conductor of inner radius 4a and outer radius 5a. Assume  
the cable to be infinitely long and its axis to be along the z-axis.  
Current flows with uniform density in the +z-direction in the inner  
conductor and returns with uniform density in the –z-direction in  
the outer conductor. Find  
everywhere and plot Hφ versus r  
H
Trần Quang Việt – BMCS – Khoa Điện – ĐHBK Tp.HCM  
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