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Physics 2220
Second Exam
Summer 2013
(Chs 27 -30)
Name:
5'0
Hassan Allami (NS 204)
Circle your Discussion TA:
Friday 12· July
L'-'l-rJo NS
Peter Peroncik (NS 203)
Mei Hui Teh (LCB 225)
You may use your one sheet of notes and formulas, but you must not collaborate with any
other person. Do all four problems, showing your method and working clearly (a correct answer
alone is not necessarily sufficient). Be sure to include correct SI units in your answers where
appropriate. The number of marks for each part is given in square brackets, [ ], to its right.
1. (The density of copper is 8.92 g/cm 3 , its molecular mass is 6.35 glmo1, its resistivity at 20°C
is 1.7 X 10- 8 n.m, and its temperature coefficient of resistivity is 3.9 x 10- 3 (oCrl. Avogadro's
number is 6.02 x 10 23 mol-I, and the fundamental charge is e ::::: 1.60 X 10-19 C.)
A copper wire of diameter 2.94 mm is 201 m long. In parts (a) and (b), assume that the
temperature is 20 0 C.
(a) Calculate the resistance of the wire. [4]
(b) If a potential difference of6.35 V is applied across the ends of the wire, fmd:
(i) the current in the wire;
[2]
(ii) the magnitude of the electric field (assumed uniform) in the wire;
[2]
(iii) the magnitude of the current density iri the wire; [2]
(iv) the drift speed of the electrons in the wire, assuming that each copper atom contributes
[6]
one free electron to the current;
(v) the time needed for the equivalent of one food calorie (4186 J of energy) to be dissipated
as heat in the wire.
[4]
(c) At what temperature would the resistance of the wire be 78 per cent greater than its value at
20°C?
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Physics 2220, Summer 2013
Name:
Second Exam
Circle TA:
2.
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Hassan
Peter
Mei Hui
93 mF in the circuit at the right; The battery has no internal resistance, and the capacitor is initially uncharged when the switch S is closed at time t
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= O.
(a) Calculate R eq' the resistance of a single
resistor that would be equivalent to the array of
four resistors shown in the figure.
c
[6]
(b) What is the total current supplied by the battery immediately after the switch S is closed?
[8]
Also, specifY clearly the current through each of the four individual resistors at this time.
(c) Just after the switch is closed, does any current flow through the wire connecting points B
and D? Give a physical reason for your answer. Ifthere is such a current, specifY its value and its
direction of flow.
[4]
(d) At what time t after the switch is closed will the capacitor be charged to 81 per cent of its
final total energy?
[8]
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Physics 2220, Summer 2013
Name:
Second Exam
Circle TA:
Hassan
..
rectangular slab of conducting material being used in a Hall
f.
effect experiment. The current I is in the direction shown,
e
,.
and the magnetic field B points perpendicularly out of the
paper. When the Hall voltage VH is measured, it is found
•
..
."
that the left-hand edge of the slab of material is at higher
answer below, indicate whether the sign of the free charge
(i) positive
-4
~
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•
potential than the right-hand edge. By circling the correct carriers in this case is:
Mei Hui
-/ ~:r
(a) The sketch at the right shows the top view of a
3.
Peter
1\
:r:. [4] (ii) negative
(iii) neither
(iv) impossible to tell without more information
(b) A deuteron has the same electric charge (+ e) as a proton, but it has twice the proton's mass.
If a proton and a deuteron are both accelerated through the same potential difference V and are
injected at right angles into a uniform magnetic field of magnitude B:
(i) How will the radii of their circular orbits compare?
[6]
(ii) How will their orbital periods compare?
[4]
(c) A horizontal wire oflength 62.0 cm and mass
and is suspended by a pair of flexible leads, as shown
x~x
in the figure at the right. What are the magnitude and
X
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Physics 2220, Summer 2013
Name:
Second Exam
Circle T A:
tA
Hassan
-r
f)
JJ s
Peter
Mei Hui
4. (a) A long wire along the x-axis carries
current I and is at one point bent into a
circular loop of radius 2R in the xy-plane, as
shown in the sketch at the right. A separate
1-- - --­
long straight wire that passes through the
-; ~
origin carries equal current I in the positive
,­
z-direction (i.e., in the direction of the unit
/'
vector k, pointing perpendicularly out of the
/'
paper). In tenus of J.l.o' I, R, and appropriat~ '\_
-
on,
unitvector(s):
/I"
. _, ~
/'
~
" ' : t : . ~ :x:
&
~
:t
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~
~ JtR ----:11171
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.,
(i) Find the resultant magnetic field B at the centre ofthe loop of wire caused by the current
in the first wire only (not the current in the wire along the z-axis).
[6]
(ii) Give the (vector) magnetic dipole moment, J.L, of the circular loop, and calculate the
(vector) torque,
't,
that acts on it due to the magnetic field produced by the wire that lies along the
z-axis. From the perspective of an observer in the xy-plane looking from the origin towards the
loop, is it being twisted clockwise or anticlockwise?
[12]
(b) A solenoid 1.30 m long and 1.30 cm in radius carries a current of 18.0 A. The magnetic field
inside the solenoid is 23.0 mT. Calculate the length of the wire forming the solenoid. (The
permeability of free space is J.l.o = 4n x 10-7 T·m/A,)
[8]
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Name:
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