Question

Electromagnetic field

Electric and magnetic fields in vacuum.

(a)Consider a region of space free from matter and from magnetic fields.Show that it cannot be permeated by an electric field of the form:

\vec{E}(x, y, z)=\frac{A}{2}(y \hat{x}-x \hat{y}+z \hat{z})

\text { where } A \text { is a constant value different from zero and with units } \mathrm{V} / \mathrm{m}^{2} \text {. }

Now, consider that a magnetic field permeates the region of space in(a). Write an expression representing a time-varying magnetic field B(r,y, z, t) that renders the vector field proposed in (a) suitable to describe an electric field. Check and demonstrate that the expression you found is a suitable representation of a magnetic field.

Hence or otherwise, show that:

\vec{B}=K x \hat{x}+K y \hat{y}+A t \hat{z}

\text { is not an adequate expression for a magnetic field for } K \neq 0 \mathrm{~T} / \mathrm{m}^{2} \text {. }  Verified  ### Question 44810  Electromagnetic field

5. Suppose we have a single conductor, as would be used for a wave guide, in the shape below. Would it be possible to use this as a transmission line under low frequency, such that the device size is much shorter than the wavelength? Why or why not? Hint: what are the physical requirements for a resistor,capacitor, and inductor in a TL?

### Question 44809  Electromagnetic field

4. Suppose we have a pair of parallel plates that we wish to use as a transmission line. The dielectric medium between the plates is air: €0, Ho. l is the length of the line, w is the width of the plates, and d isthe separation between the plates.
(a) Find an expression for C'.
(b) Find an expression for L'.
(c) Plot how the signal velocity v changes as a function of d.

### Question 44808  Electromagnetic field

3. Assume that we have a lossless waveguide of width a, height b surrounding a dielectric medium with€, Ho. We want to discuss an input signal with frequency w, sufficiently large for a TE11 operating mode.
(a) Find the group velocity of the resulting wave.
(b) Find the phase velocity of the resulting wave.(
(c) What conditions for a, b would allow the group and phase velocities to converge? What physical meaning does this limit have? Hint: focus on the waveguide's influence on the medium.

### Question 44807  Electromagnetic field

2. Assume that we have a transmission line with characteristic impedance zo, with an insulator between the plates withe, Ho. We continuously input a waveform with an amplitude Vo and frequency w such that the TL length I contains exactly one wavelength.Assume load impedance z, is in open condition. Assume the generator is in matched condition, i.e. the input impedance is equal to zo.
(a) Plot the forward and reverse voltage wave forms at the given timestamps on the left axes below.To is the transit time for the length of the TL. Make sure to distinguish between forward and reverse lines.
(b) Do the same as in part (a), but for the forward and reverse current wave forms on the right axes.
(c) What is To in terms of the given TL parameters?

### Question 44806  Electromagnetic field

1. Consider a plane wave propagating along the z-axis towards the boundary between two insulators, as shown below.
(a) What is I if the incident wave comes from the left?
(c) Compare the magnitudes of I in both cases. Should they be the same? Why or why not?

### Question 44593  Electromagnetic field

### Question 44592  Electromagnetic field

Match the following according to the type of motor load:

### Question 44591  Electromagnetic field

Chose the best motor type which suits each of the following applications:

### Question 44590  Electromagnetic field

Explain in brief the principle of AC synchronous and induction motors.

### Question 44589  Electromagnetic field

DC motors use permanent magnets to construct a static magnetic field.
If a motor consumes 184 kW of power but only produces 231 HP at the shaft, itscurrent operating efficiency isanswer to the nearest one.% (1 Horsepower = 745.7 Watts). Round your
c) Induction motors use commutators to transmit current to the rotor, thus producing a rotor magnetic field.
A live reading of a motor indicates that it is consuming 16.4 kVA with a Power Factor of 0.76. You also know the current operating efficiency of the motor is 89%. What is the instantaneous power output of the motor? (1 Horsepower = 745.7 Watts).

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