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Calculate work done by expanding gas of 1 mole if initial pressure is 4000
Pa, initial volume is 0.2 m3.
Assume a two processes: (1) isobaric expansion to 0.3 m3 (2) isothermal
expansion to 0.3 m3.
1. Isobaric expansion:
W  PV  P V f  Vi   4000 Pa  0.3m3  0.2m3 
 400 J
Also:
Pf V f
3
0.3
m
nR 


 1.5
3
PV
Ti
Vi 0.2m
i i
nR
Tf
Vf
A 50% increase in temperature!
2. Isothermal expansion:
W
Vf
Vf
Vi
Vi
 PdV  
nRT
dV
V
 Vf 
 Vf 
 nRT ln    PV

i i ln 
V
V
 i 
 i 
0.3m3
3
  4000 Pa   0.2m  ln
 324 J
3
0.2m
Also:
Vi
0.2m3
Pf  Pi
 4000 Pa
 2667 Pa
3
Vf
0.3m
A ~67% decrease in pressure!
A
An infinitely long wire, as shown in the figure, is uniformly charged with
density of λ. The radius of the ¼ circle is R. Find the electric field at O.
∞
R
y  R tan  , r 
y
cos 
∞
1  dy
dE 
(cos  iˆ  sin  ˆj )
2
4 0 r
A θ O
x
θ
1 

(cos  iˆ  sin  ˆj )d
4 0 R
B
 /2

E1 
0

4 0 R
(cos  iˆ  sin  ˆj )d
 ˆ ˆ
(i  j )
1
4 0 R
E2 
B∞

1
1

4 0 R
(iˆ  ˆj )
E  E1  E 2  E3
1  Rd
(cos  iˆ  sin  ˆj )
2
4 0 R
 /2
1  Rd
ˆ  sin  ˆj )   (iˆ  ˆj )
E3  
(cos

i
4 0 R 2
4 0 R
0
dE 
AB
∞
A uniformly charged sphere (charge density of ρ) with a sphere hole inside is
shown in the figure. Find the electric field intensity at the center of the hole.
1
Filled:
 E  dS    q
i
0
s
i
4
  ( d  r )3
E1 4 (d  r ) 2  3
0
 (d  r )
E1 
3 0
Contribution from filled part:
E2  0
 (d  r )
E  E1  E2 
3 0
O
d
r
Two point charges (q and -2q) are located at x=1m and x=-1m, respectively.
Another point charge is located on the X axis. What is the position of this charge
so that the net electric force on it is zero?
q
4 0  x  1
2

2q
4 0  x  1

x  3 2 2

x  3  2 wrong!

x  3 2 2

2
0
Find the magnetic field intensity at P.
I
30o
30o
B  B1  B2

0 I
4r
[sin 60  sin(90)] 
0 I
4r
[sin 90  sin(60)]
r =0.1 cm
P
An electron is passing A with a speed of 104 m/s in a perpendicular magnetic field.
Find the radius of the electron’s circular motion and the frequency of the cyclotron.

v
 F  qvB  m v R
2
mv
R 
qB
frequency
A
v
qB
f 

2 R
2 m

B
A straight long wire with current I is placed beside a metallic trapezoid .
ab=bc=ad=L. Distance between point d and the wire is l. The trapezoid freely
falls a height H from still.
Find 1) the instant induced current in the trapezoid when it falls H.
2) the potential difference between dc at that moment.
I 0
dc  2L
a
c
Vdc   (v  B)  d l   vB d l
d
d
2L




0 I
2
l
c
2 gH 
0 I
2(r  l )
l  2L
2 gH ln
l
dr
b
60°60o c
d
I
H
A setup of double-slit interference is shown below. D=1.2m, d=0.45mm. If the
distance between adjacent bright lines on the screen is 1.5mm. Find the wavelength
of the source light.
P
S1
S

d
D
S2
△x
 d sin 
d sin   n
d sin  '  (n  1)
D
y  D(tan  ' tan  )  D(sin  ' sin  ) 
d
d y

 ...
D
In experiment of Fraunhofer diffraction from a single slit, f = 0.5m，=5000Å，
the width of the slit a=0.1mm. Find the width of central maximum
P1
asin =2( /2)
the width of central maximum
2 x  2 f tg 1
 2 f sin1
2f

a
x
0
1
f
A space craft with a proper length of L0=90m moves at v=0.8c with respect to one
observer. Measured by the observer, What is the time interval between the craft’s
head and end passing through the observer?
L  L0 1  (v / c) 2  54m
△t1 = L/v =2.25×10-7 s