Question

Electromagnetic field

Q1 A hollow spherical conductor of internal radius R2 and external radius R3surrounds a conductive sphere of radius R1, which is charged with a charge Q,as shown in Figure Q1.

Derive the expression for the magnitude of the electric field E(r), for r between 0 and o. Note that r = 0 is the origin of the spherical reference system, as shown in Figure Q1.

hence or otherwise, derive the expression for the scalar potential V (r),between 0 and infinity

Give a qualitative graphical representation for the functions E(r)(magnitude of the electric field) and V(r) (scalar potential), considering R1 = 30 cm, R2Use the appropriate emits on the graphs. Write the values of the electric field in the dielectric side of the interface for each of the metallic50 cm, R3 = 80 cm, and Q= 800 x 10-12 C.surfaces. Write the values for the potential at r = 0, r =R1, r = R2,and r == R3.

Briefly describe what happens to the scalar potential and electric field in the region with R <r< R2 at the static equilibrium if a charged sphere of radius R, =close to the hollow conductor, with its centre at R4 4 m. Include a brief explanation for your answer.20 cm and charge Q. 10-6 C is positioned

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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).