无代写-ELEC0005 2019
时间:2022-04-26
(Old code ELEC104P) ELEC0005 2019
Page 1 of 7 TURN OVER
List of Physical Constants:
Electronic charge: e = 1.60 × 10−19 C
Permittivity of vacuum or air: o = 8.85 × 10-12 F∙m-1
Permeability of vacuum or air: o = 4 × 10-7 H∙m-1
Answer ALL the questions in Section A. Answer TWO questions from Section B
There is a formula sheet on page 7.
SECTION A (There are EIGHT questions in this section)
1. Identify the quantities in the following list that are (a) vectors and (b) vector fields.
[6 marks]
(i) Velocity of a ball
(ii) Acceleration of a train
(iii) Gravity around the earth
(iv) Magnetic Field around a solenoid
(v) Position of a point relative to another point
(vi) Force on an electron in an electric field.
2. Sketch the electric field, E, inside and outside a thin, spherical shell with a charge Q
evenly distributed over the surface of the shell. Both inside and outside the shell is a
vacuum, so that εr = 1. Explain your answer.
[6 marks]
3. What happens to an insulator when it is placed in an electric field?
[6 marks]
4. By using Gauss’ law (magnetic), equation [5] on the formula sheet, derive the
conditions on the normal (perpendicular) component of the magnetic flux density,
B, at the surface of a magnetic material with a relative permeability of µr. Explain
the steps in your answer. [7 marks]
(Old code ELEC104P) ELEC0005 2019
Page 2 of 7 CONTINUED
5. By considering the potential difference between two points close together on an
equipotential surface in a region of an electric field, E, show that the electric field
must be at right angles to the equipotential surface. The potential difference is given
by equation [3] on the formula sheet.
[6 marks]
6. A solenoid has a time varying current flowing through the coil. Three different
loops of wire are wound around the solenoid. The wires are made from copper, a
resistive alloy and a graphite loaded filament; they have resistance values of Rc, Ra,
Rg respectively. The values are such that Rc < Ra < Rg. What are the relative values
of the electromotive force (e.m.f) in each loop? Justify your answer.
[6 marks]
7. An n-channel MOSFET is made using an oxide that is 2 nm thick and has a relative
permittivity of 4. The channel is 90 nm long and 900 nm wide. The electron and
hole mobilities in the channel are 1500 cm2 ∙ V-1 ∙ s-1 and 450 cm2 ∙ V-1 ∙ s-1,
respectively and the threshold voltage is 1 V. Calculate the device transconductance
parameter gn, and suggest how it could be doubled without changing the fabrication
process technology.
[7 marks]
8. An NPN bipolar junction transistor is operated in the active state. Use a diagram to
indicate the flow of electrons and holes between the base, collector and emitter
(making sure to label each part) and write down the bias state (i.e. forward or
reverse biased) of each of the PN junctions.
[6 marks]
(Old code ELEC104P) ELEC0005 2019
Page 3 of 7 TURN OVER
SECTION B Answer TWO out of FOUR questions from this section.
9. (a) State Gauss’ law (electric) in words. [3 marks]
(b) A conductor can have a surface charge density of σ Cm-2 at the surface of the
conductor.
(i) Using Gauss’ Law (equation [6] on the formula sheet at the end of the
paper) derive the boundary condition on the normal component of the
electric flux density D at the surface of a conductor. Assume a surface
charge density of σ Cm-2 on the surface. Explain the steps carefully.
[6 marks]
(ii) Sketch the electric flux density around a charged disc, showing the field
both close to the disc and at a distance. (You may prefer to use two
sketches.)
[4 marks]
(iii)A thin disc is uniformly charged with 5.0 µC distributed over both surfaces.
The radius of the disc is 0.3 m. What is the approximate magnitude of the
electric flux density at a distance of (A) 1mm from the centre of the flat
surface and (B) 25 m from the disc? (εr = 1)
[5 marks]
(c) A thundercloud can be approximated as a dipole, oriented with the axis at right
angles to the surface of the earth. The earth’s surface can be taken, over a region, to
be a flat conducting surface.
(i) Explain briefly how the method of images is used.
(ii) A thundercloud forms between the heights of 5 km and 8 km above the
ground and can be considered to be a dipole of charges arranged as follows:
+10 C at 8 km and -10 C at 5km, at either end of the cloud. Using the
method of images, what is the electric flux density (D) on the ground, just
below the thundercloud?
[7 marks]
(Old code ELEC104P) ELEC0005 2019
Page 4 of 7 CONTINUED
10. (a) Sketch the electric flux density around a line charge of charge density q Cm-1,
explaining the key features of the diagram.
[6 marks]
(b) The electric flux density, D, at a distance R away from a line charge (line charge
density of q Cm-1) is given by the equation:
2
R
q
R
=D a equation 10.1
where Ra is a unit vector in the radial direction. Two identical line charges with
charge density 20 µCm-1, are placed along the x axis and the y axis. What is the
electric flux density at position given by coordinate (3, 3, 3) m?
[7 marks]
(c) A single line charge is placed along the x-axis.
(i) What is the potential difference between two points, R1 = 1 cm and R2 = 3
cm along a radial direction away from a single line charge of 10 μC∙m-1?
The electric flux density is given by equation 10.1, the co-ordinates of the
two points are R1 = (1,0,0) and R2 = (3,0,0). The points are in a vacuum, so
εr = 1.
[5 marks]
(ii) What is the potential difference if the line charge is placed inside and along
the axis of a cylinder of dielectric of value ε = 3 and of radius 2 cm?
[3 marks]
(iii)Sketch the electric field distribution in the cylinder and dielectric and
outside the cylinder.
[4 marks]
(Old code ELEC104P) ELEC0005 2019
Page 5 of 7 TURN OVER
11. (a) The mutual inductance, M, of two single loops of conducting wire, 1 and 2, is given
by 12
1
M
I
= , where current I1 is flowing in loop 1 and 12 is the magnetic flux
from coil 1 linking into loop 2.
(i) How is the definition altered for the self-inductance of a loop?
(ii) What is the self-inductance of a solenoid, with N loops per unit length of
radius a? The magnetic field inside a solenoid with current I flowing in it is
NI.
[9 marks]
(b) A magnetic core material has two coils (numbered 1 and 2) wound around it (figure
11.1). The lower coil (coil 1) has a battery connected to through switch S1, which
is closed at t = 0. Then at t = t1 the second switch S2 is closed, giving a short circuit
across the coil.
Figure 11.1
(i) The current I1 in coil 1, does not increase instantaneously to its
maximum value when the switch S1 is closed at t = 0, nor
decrease to zero when S2 is closed at t = t1. Explain why.
(ii) Sketch the current I2 in the second coil as a function of time.
(iii) Which of the quantities L1, L2 and M , does the current I2 depend
on and why?
(iv) What is the effect of the magnetic core material?
[16 marks]
R2
R
1
I
1
S1
S2
t=0
t=t1
I
2
L1 self-inductance of loop 1
L
2 self-inductance of loop 2
M mutual inductance of the loops 1 and 2
(Old code ELEC104P) ELEC0005 2019
Page 6 of 7 CONTINUED
12. (a) Define mobility in the context of electrical conduction, giving two physical
contributions to electron mobility in materials. [3 marks]
(b) Estimate the drift velocity of electrons in a 10 μm long strip of graphene across
which a voltage of 100 mV has been applied, giving units. Assume the mobility of
electrons in the graphene to be 100,000 cm2 ∙V-1 ∙s-1. [5 marks]
(c) Show that the conductivity, σ, of an n-type semiconductor can be expressed as:
= ( +
2ℎ
) ,
where μe is the electron mobility, μh the hole mobility, ND is the donor
concentration and ni is the intrinsic carrier concentration. [4 marks]
(d) For donor concentrations greater than 1011 cm-3 explain why the contribution of
holes to the conductivity of n-type silicon can be neglected (ni(Si) ≈ 1010 cm-3 at
room temperature). [2 marks]
(e) Figure 12.1 shows the conductivity of a variety of n-type Si samples as a function
of donor concentration, at two different temperatures, 300 K and 100 K.
(i) From the data, estimate the electron mobility in intrinsic Si material at
300 K. [5 marks]
(ii) Estimate the electron mobility in intrinsic Si material at 100 K, and
comment on the answer with respect to the mobility at 300 K, giving
a physical reason. [4 marks]
(iii) Give a reason why the conductivity plot shown in Figure 12.1 is not a
linear function of doping concentration. [2 marks]
Figure 12.1
(Old code ELEC104P) ELEC0005 2019
Page 7 of 7 END OF PAPER
FORMULA SHEET
The symbols have the usual meaning.
[1] Permittivity D = 0E + P = 0rE
[2] Permeability B = μr μo H and B = 0 (H + M)
[3] Electric potential between A and B −=−
A
B
BA dVV cE
[4] Ohm’s law J=E
[5] Gauss’ law (magnetic) 0=
S
dSB
[6] Gauss’ law (electric) =
VS
dvd SD
[7] Continuity of charge −=
+ V'SS
dv
dt
d
d SJ
[8] From the Biot-Savart law
=
2
0
4 r
I
d r
udl
B
[9] The Lorentz force: BvEF += QQ
[10] Maxwell via Ampère’s law: +=
SSc
d
dt
d
dd SDSJcH
[11] Faraday’s law −=
Sc
M d
dt
d
d SBcE
[12] MOSFET transconductance parameters =
(
), = ℎ
(
)
[13] MOSFET I-V relationship IDS = gn VOV -
1
2
VDS
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÷VDS