EN1084 Electromagnetics & Electronic Materials Autumn 2021 / 2022
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EN1084
Electromagnetics & Electronic Materials
Autumn 2021 / 2022
Q1. a) Define the terms “electric field” E and “electric potential” 0. Also explain how they are related to each other, illustrating your discussion with a labelled diagram of the electrostatic field of two equal, positive point charges. [6 marks]
b) Point charges of +4pC and -3pC are held at the points A(0,0)cm and B(2,0)cm, respectively. Calculate the forces (as row vectors) on each of the two charges, indicating the force directions with a sketch. [5 marks]
c) Calculate the electric field (as a row vector) at the point C(2,2)cm, and hence calculate its magnitude and angle to the positive x axis (illustrate your workings with a vector diagram). [10 marks]
d) Calculate the electric potential at the point C(2,2)cm, and hence the work done in moving a third point charge +5pC to point C from a very long distance away. [4 marks] 25 Marks
Q2. a) Explain why the static electric field is always zero inside an isolated conductor. What is the consequence of this for the electric field at the surface of the conductor? [3 marks]
b) A square, thin aluminium plate has dimensions of 20 mm × 20 mm × 0.3 mm. It carries a charge of + 17pC.
(i) How many electrons have been transferred in charging the plate, assuming its initial charge was 
5pC. [2 marks]
(ii) Sketch the distribution of electric field and equipotential surfaces in the space outside the plate, labelling the important features. [4 marks]
(iii) Stating any approximations you make, estimate the electric field magnitude on the surface of the plate. [3 marks]
(iv) Again stating any approximations you make, estimate the electric field magnitude and electric potential a distance of 10m from the plate. [3 marks]
c) The plate is now placed parallel to a large, flat aluminium plate, held at an electric potential of 
4.5V. Assume that no charge has been lost and that the plates have a final (constant) separation of 1.5mm.
(i) Estimate the electric field magnitude between the plates and hence estimate the voltage across the plates, stating your approximations. [4 marks]
(ii) Sketch the electric field distribution and equipotential surfaces in and around the plates, labelling the important features. [4 marks]
(iii) Determine precisely where the electric potential is zero. [2 marks] 25 Marks
Q3. a) Dielectrics are class of material, capable of storing energy by polarisation in the presence of an applied electric field.
(i) The relative permittivity (or dielectric constant) is a dimensionless quantity relating the dielectric properties of a material to those of a vacuum. Explain briefly why it is that polar dielectrics typically exhibit higher relative permittivity than non-polar dielectrics. [4 marks]
(ii) With the aid of diagrams, describe any two of the principal polarising mechanisms in a dielectric material, [6 marks]
(iii) Why does the relative permittivity and loss change with the frequency of the applied electric field, and what is meant by the term relaxation frequency? Can you suggest an application where a high dielectric loss tangent might be desirable? [5 marks]
b) A high-energy capacitor consists of a pair of parallel metallic plates, separated by a paper layer, rolled up and immersed in a liquid dielectric. The dielectric is a mineral oil, and the combined paper-oil dielectric is found to have a dielectric strength of 6 × 107 V/m , relative permittivity 3.3 and volume resistivity 3 × 109 Ωm.
(i) If the spacing between the plates is 0.6mm, determine the maximum theoretical operating voltage of this capacitor. Explain why you should avoid operating close to this voltage. [3 marks]
(ii) The total capacitance is measured to be 58.4nF. Estimate the effective cross-sectional area of the plates. [2 marks]
(iii) Assuming the relative permittivity of the dielectric remains unchanged, calculate its loss tangent at a frequency of 1MHz. [2 marks]
(iv) Suggest two ways of increasing the energy storage capacity of this capacitor design and explain your reasoning. [3 marks] 25 Marks
Q4. a) With the aid of suitable labelled diagrams, describe the processes of carrier generation and recombination in a semiconductor. [6 marks]
b) Explain what is mean by the “mobility” of carriers in a conducting material, why electron mobilities are higher for electrons than holes, and why electron mobilities are higher in semiconductors like silicon than in a highly conducing metal like copper. [4 marks]
c) Explain how the electrical conductivity of a material depends on the free carrier density and carrier mobility, and hence describe and explain the differences in the temperature dependences of the conductivity of an intrinsic semiconductor (e.g. pure silicon) compared with a good metal (e.g. copper). [4 marks]
d) A silicon wafer has a p-type feature on its surface, with an acceptor density of NA = 7.5 × 1021 per m3, a length of 200
m and cross-sectional dimensions of 15
m × 0.9
m. A voltage of 1.5V is applied across its length.
(i) Calculate the conductivity of the p-type silicon, hence the drift current density and the total drift current along the length of the doped feature. [5 marks]
(ii) Calculate the sheet resistance of the p-type silicon and the resistance of the doped feature. [3 marks]
(iii) If the same p-type silicon is used in a pn diode with a built-in voltage of 0.70V, calculate the n-type doping density that is required. [3 marks] 25 Marks
2023-06-07