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engineering
electrical engineering

Questions and Answers of Electrical Engineering

A line of charge of uniform density occupies a semicircle of radius b as shown in the figure. Use the material presented in Example 4-4 to determine the electric field at the origin.
A spherical shell with outer radius b surrounds a charge-free cavity of radius aWhere v0 is a positive constant, determine D in all regions.
Two infinite lines of charge, both parallel to the z-axis, lie in the x€“z plane, one with density l and located at x €“ a and the other with density l and located
A cylinder-shaped carbon resistor is 8 cm in length and its circular cross section has a diameter d – 1 mm.(a) Determine the resistance R.(b) To reduce its resistance by 40%, the carbon resistor is
A coaxial capacitor consists of two concentric, conducting, cylindrical surfaces, one of radius a and another of radius b, as shown in the figure. The insulating layer separating the two conducting
An electron with a speed of 8 x 106 m/s is projected along the positive x-direction into a medium containing a uniform magnetic flux density B = (x4 _ z3) T. Given that e =1.6 x 10 –19 C and the
When a particle with charge q and mass m is introduced into a medium with a uniform field B such that the initial velocity of the particle u is perpendicular to B, as shown in Fig. 5-31 (P5.2), the
The circuit shown in Fig. 5-32 (P5.3) uses two identical springs to support a 10-cm-long horizontal wire with a mass of 20 g. In the absence of a magnetic field, the weight of the wire causes the
The rectangular loop shown in Fig. 5-33 (P5.4) consists of 20 closely wrapped turns and is hinged along the z-axis. The plane of the loop makes an angle of 30o with the y-axis, and the current in the
In a cylindrical coordinate system, a 2-m-long straight wire carrying a current of 5 A in the positive z-direction is located at r = 4 cm,  2, and, 1 m (a)
A 20-turn rectangular coil with side l = 20 cm and w = 10 cm is placed in the y€“z plane as shown in Fig. 5-34 (P5.6).(a) If the coil, which carries a current I =10 A, is in the presence of
An 8 cm x 12 cm rectangular loop of wire is situated in the x–y plane with the center of the loop at the origin and its long sides parallel to the x-axis. The loop has a current of 50 A flowing
Use the approach outlined in Example 5-2 to develop an expression for the magnetic field H at an arbitrary point P due to the linear conductor defined by the geometry shown in Fig. 5-35 (P5.8). If
The loop shown in Fig. 5-36 (P5.9) consists of radial lines and segments of circles whose centers are at point P. Determine the magnetic field H at P in terms of a, b, , and I.
An infinitely long, thin conducting sheet defined over the space 0
An infinitely long wire carrying a 25-A current in the positive x-direction is placed along the x-axis in the vicinity of a 20-turn circular loop located in the x€“y plane as shown in Fig.
Two infinitely long, parallel wires carry 6-A currents in opposite directions. Determine the magnetic flux density at point P in Fig. 5-38 (P5.12).
A long, East-West oriented power cable carrying an unknown current I is at a height of 8 m above the Earth’s surface. If the magnetic flux density recorded by a magnetic-field meter placed at the
Two parallel, circular loops carrying a current of 40 A each are arranged as shown in Fig. 5-39 (P5.14). The first loop is situated in the x–y plane with its center at the origin and the second
The long, straight conductor shown in Fig. 5-40 (P5.15) lies in the plane of the rectangular loop at a distance d = 0.1 m. The loop has dimensions a = 0.2 m and b =0.5 m, and the currents are I1 = 20
In the arrangement shown in Fig. 5-41 (P5.16), each of the two long, parallel conductors carries a current I, is supported by 8-cm-long strings, and has a mass per unit length of 1.2 g/cm. Due to the
An infinitely long, thin conducting sheet of width w along the x-direction lies in the x–y plane and carries a current I in the _ y-direction. Determine (a) The magnetic field at a point P midway
Three long, parallel wires are arranged as shown in Fig. 5-43 (P5.18 (a)). Determine the force per unit length acting on the wire carrying I3.
A square loop placed as shown in Fig. 5-44 (P5.19) has 2-m sides and carries a current I1= 5 A. If a straight, long conductor carrying a current I2 = 10 A is introduced and placed just above the
Current I flows along the positive z-direction in the inner conductor of a long coaxial cable and returns through the outer conductor. The inner conductor has radius a, and the inner and outer radii
A long cylindrical conductor whose axis is coincident with the z-axis has a radius a and carries a current characterized by a current density J = zJ0/r, where J0 is a constant and r is the radial
Repeat Problem 5.21 for a current density J = z joe€“r
In a certain conducting region, the magnetic field is given in cylindrical coordinates byFind the current density J.
With reference to Fig. 5-10, (a) Derive an expression for the vector magnetic potential A at a point P located at a distance r from the wire in the x–y plane, and then (b) Derive B from A. Show
In a given region of space, the vector magnetic potential is given by A =x5cosy + z(2+sinx) (Wb/m). (a) Determine B. (b) Use Eq. (5.66) to calculate the magnetic flux passing
A uniform current density given byJ = zj0 (A/m2)Gives rise to a vector magnetic potential(a) Apply the vector Poisson€™s equation to confirm the above statement.(b) Use the expression for A
A thin current element extending between z = _ L/2 and z =L/2 carries a current I along z through a circular cross section of radius a.(a) Find A at a point P located very far from the origin (assume
In the model of the hydrogen atom proposed by Bohr in 1913, the electron moves around the nucleus at a speed of 2 x 106 m/s in a circular orbit of radius 5 x 10-11 m. What is the magnitude of the
Iron contains 8.5 x 1028 atoms/m3 at saturation the alignment of the electrons’ spin magnetic moments in iron can contribute 1.5 T to the total magnetic flux density B. If the spin magnetic moment
The x€“y plane separates two magnetic media with magnetic permeabilities μ1 and μ2, as shown in Fig. 5-45 (P5.30). If there is no surface current at the interface and the magnetic
Given that a current sheet with surface current density Js = ˆx8 (A/m) exists at y = 0, the interface between two magnetic media, and H1 = z11 (A/m) in medium 1 (y > 0), determine H2 in medium 2(y <
In Fig. 5-46 (P5.32), the plane defined by x y = 1 separates medium 1 of permeability μ1 from medium 2 of permeability μ2. If no surface current exists on the boundary and B1 = x2 + y3
The plane boundary defined by z = 0 separates air from a block of iron. If B1 = x4 – y6 z8 in air (z > 0), find B2 in iron (z < 0), given that μ = 5000μ0 for iron
Show that if no surface current densities exist at the parallel interfaces shown in Fig. 5-47 (P5.34), the relationship between 4 and 1 is independent of μ2.
Obtain an expression for the self-inductance per unit length for the parallel wire transmission line of Fig. 5-27(a) in terms of a, d, and μ, where a is the radius of the wires, d is the
A solenoid with a length of 20 cm and a radius of 5 cm consists of 400 turns and carries a current of 12 A. If z = 0 represents the midpoint of the solenoid, generate a plot for H (z) as a function
In terms of the d-c current I, how much magnetic energy is stored in the insulating medium of a 3-m-long, air-filled section of a coaxial transmission line, given that the radius of the inner
The rectangular loop shown in Fig. 5-48 (P5.38) is coplanar with the long, straight wire carrying the current I = 20 A. Determine the magnetic flux through the loop
A circular loop of radius a carrying current I1 is located in the x€“y plane as shown in the figure. In addition, an infinitely long wire carrying current I2 in a direction parallel with
A cylindrical conductor whose axis is coincident with the z-axis has an internal magnetic field given byWhere a is the conductor€™s radius. If a =5 cm, what is the total current flowing in
Determine the mutual inductance between the circular loop and the linear current shown in the figure.
The switch in the bottom loop of Fig. 6-17 (P6.1) is closed at t = 0 and then opened at a later time t1. What is the direction of the current I in the top loop (clockwise or counterclockwise) at each
The loop in Fig. 6-18 (P6.2) is in the x–y plane and B = zB0 sint with B0 positive. What is the direction of I (or = ) at (a) t = 0, (b) t =
A coil consists of 100 turns of wire wrapped around a square frame of sides 0.25 m. The coil is centered at the origin with each of its sides parallel to the x- or y-axis. Find the induced emf across
A stationary conducting loop with internal resistance of 0.5 is placed in a time-varying magnetic field. When the loop is closed, a current of 5 A flows through it what will the
A circular-loop TV antenna with 0.02 m2 area is in the presence of a uniform-amplitude 300-MHz signal. When oriented for maximum response, the loop develops an emf with a peak value of 30 (mV). What
The square loop shown in Fig. 6-19 (P6.6) is coplanar with a long, straight wire carrying a current I(􀀀t) = 5cos 2104t (A)(a) Determine the emf induced across a small gap
The rectangular conducting loop shown in Fig. 6-20 (P6.7) rotates at 6,000 revolutions per minute in a uniform magnetic flux density given by B = y50 (mT) Determine the current induced in the loop if
A rectangular conducting loop 5 cm 10 cm with a small air gap in one of its sides is spinning at 7200 revolutions per minute. If the field B is normal to the loop axis and its magnitude is 6 x 10–6
A 50-cm-long metal rod rotates about the z-axis at 90 revolutions per minute, with end 1 fixed at the origin as shown in Fig. 6-21 (P6.9). Determine the induced emf V12 if B = z2 x 10–4 T.
The loop shown in Fig. 6-22 (P6.10) moves away from a wire carrying a current I1 = 10 (A) at a constant velocity u = y7.5 (m/s). If R = 10 and the direction of I2 is as defined in the
The conducting cylinder shown in Fig. 6-23 (P6.11) rotates about its axis at 1,200 revolutions per minute in a radial field given by B = r6 (T) The cylinder, whose radius is 5 cm and height 10 cm,
The electromagnetic generator shown in Fig. 6-12 is connected to an electric bulb with a resistance of 150 . If the loop area is 0.1 m2 and it rotates at 3,600 revolutions per minute in a
The circular disk shown in Fig. 6-24 (P6.13) lies in the x€“y plane and rotates with uniform angular velocity about the z-axis. The disk is of radius a and is present in a
The plates of a parallel-plate capacitor have areas 10 cm2 each and are separated by 2 cm. The capacitor is filled with a dielectric material with 40, and the
A coaxial capacitor of length l = 6 cm uses an insulating dielectric material with r =9. The radii of the cylindrical conductors are 0.5 cm and 1 cm. If the voltage applied across the
The parallel-plate capacitor shown in Fig. 6-25 (P6.16) is filled with a lossy dielectric material of relative permittivity r and conductivity . The separation between the plates is d
An electromagnetic wave propagating in seawater has an electric field with a time variation given by E = zE0 cost. If the permittivity of water is 810 and its conductivity is 4 (S/m),
At t = 0, charge density v0 was introduced into the interior of a material with a relative permittivity r = 9. If at t =1 μs the charge density has dissipated down to 103v0, what is the
If the current density in a conducting medium is given by J (x, y, z; t) = (xz2 – y4y2 + z2x) cos t determine the corresponding charge distribution v (x, y, z; t).
In a certain medium, the direction of current density J points in the radial direction in cylindrical coordinates and its magnitude is independent of both and z. Determine J, given
If we were to characterize how good a material is as an insulator by its resistance to dissipating charge, which of the following two materials is the better insulator?
The electric field of an electromagnetic wave propagating in air is given byFind the associated magnetic field H (z. t)
The magnetic field in a dielectric material with 40, μ = μ0, and 0 is given byFind k and the associated electric field E.
Given an electric fieldWhere E0, a, , and k are constants, find H.
The electric field radiated by a short dipole antenna is given in spherical coordinates byFind H (R = ; t)
A Hertzian dipole is a short conducting wire carrying an approximately constant current over its length l. If such a dipole is placed along the z-axis with its midpoint at the origin and if the
The magnetic field in a given dielectric medium is given byWhere x and z are in meters. Determine: v (a) E,(b) The displacement current density Jd, and(c) The charge density v.
The transformer shown in the figure consists of a long wire coincident with the z-axis carrying a current I = I0 cos t, coupling magnetic energy to a toroidal coil situated in the
In wet soil, characterized by 10–12 (S/m), μr = 1, and r = 36, at what frequency is the conduction current density equal in magnitude to the
In free space, the magnetic field is given by(a) Determine k.(b) Determine E.(c) Determine Jd.
The magnetic field of a wave propagating through a certain nonmagnetic material is given byFind(a) The direction of wave propagation,(b) The phase velocity,(c) The wavelength in the material,(d) The
Write general expressions for the electric and magnetic fields of a 1-GHz sinusoidal plane wave traveling in the y-direction in a lossless nonmagnetic medium with relative permittivity r = 9.
The electric field phasor of a uniform plane wave is given by E = y10ej0.2z (V/m). If the phase velocity of the wave is 1.5 x 108 m/s and the relative permeability of the medium is μr = 2 4,
The electric field of a plane wave propagating in a nonmagnetic material is given byDetermine (a) the wavelength, (b) r, and (c) H
A wave radiated by a source in air is incident upon a soil surface, whereupon a part of the wave is transmitted into the soil medium. If the wavelength of the wave is 60 cm in air and 20 cm in the
The electric field of a plane wave propagating in a lossless, nonmagnetic, dielectric material with r = 2.56 is given byDetermine:(a) f, up, , k, and , and(b) The magnetic
An RHC-polarized wave with a modulus of 2 (V/m) is traveling in free space in the negative z-direction. Write down the expression for the wave€™s electric field vector, given that the
For a wave characterized by the electric field Identify the polarization state, determine the polarization angles (and sketch the locus of E
The electric field of a uniform plane wave propagating in free space is given by E (x + jy) 20e–jz/6 (V/m). Specify the modulus and direction of the electric field intensity at the z =0
A linearly polarized plane wave of the form E = xaxe jkz can be expressed as the sum of an RHC polarized wave with magnitude aR and an LHC polarized wave with magnitude aL. Prove this statement by
The electric field of an elliptically polarized plane wave is given by Determine (a) The polarization angles (and (b) The direction of rotation.
Compare the polarization states of each of the following pairs of plane waves: (a) Wave 1: E1 = x2cos (t – kz) + y2sin (t – kz), Wave 2: E2 = x2cos (t + kz) + y2sin
Plot the locus of E (0, t) for a plane wave withDetermine the polarization state from your plot.
For each of the following combination of parameters, determine if the material is a low-loss dielectric, a quasi-conductor, or a good conductor, and then calculate , , , up,
Dry soil is characterized by r = 2.5, μr = 1, and 0 –4 (S/m). At each of the following frequencies, determine if dry soil may be considered a good conductor, a quasi-conductor,
In a medium characterized by r = 9, μr = 1, and.1 S/m, determine the phase angle by which the magnetic field leads the electric field at 100 MHz.
Generate a plot for the skin depth versus frequency for seawater for the range from 1 kHz to 10 GHz (use log-log scales). The constitutive parameters of seawater are μr = 1, r = 80 and 4 S/m.
Ignoring reflection at the air-soil boundary, if the amplitude of a 3-GHz incident wave is 10 V/m at the surface of a wet soil medium, at what depth will it be down to 1 mV/m? Wet soil is
The skin depth of a certain nonmagnetic conducting material is 3 μm at 5 GHz. Determine the phase velocity in the material.
Based on wave attenuation and reflection measurements conducted at 1 MHz, it was determined that the intrinsic impedance of a certain medium is 28.1
The electric field of a plane wave propagating in a nonmagnetic medium is given byObtain the corresponding expression for H.
In a nonmagnetic, lossy, dielectric medium, a 300-MHz plane wave is characterized by the magnetic field phasorObtain time-domain expressions for the electric and magnetic field vectors.
A rectangular copper block is 30 cm in height (along z). In response to a wave incident upon the block from above, a current is induced in the block in the positive x-direction. Determine the ratio
The inner and outer conductors of a coaxial cable have radii of 0.5 cm and 1 cm, respectively. The conductors are made of copper with r = 1, μr = 1 and

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