PHYS 241/spring2014: Assignment EXAM02SP11
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sp11ex02q07 [10 points] (Last updated: Mon Apr 11 16:54:40 2011) [meiles]
Magnetic field on the axis of solenoid Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
A solenoid 2.9 m long has a radius of 0.85 cm and 560 turns. It carries a current I of 2.5 A. What is the
approximate magnetic field B on the axis of the solenoid?
a. b. c. d. e. 0.607 mT
1.214 mT
1.172 T
3.034 mT
15.17 mT
____________________ [10 points] Maximum number of attempts for credit = 1.
sp11ex02q08 [10 points] (Last updated: Thu Apr 7 14:37:14 2011) [meiles]
Torque on a coil Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
What is the maximum torque on a 1000 turn circular coil of radius 0.75 cm that carries a current of 1.4 mA
and resides in a uniform magnetic field of 0.25 T?
a. b. c. d. e. 6.19 10­5 N ∙ m
12.37 10­7 N ∙ m
8.66 10­5 N ∙ m
1.55 10­5 N ∙ m
17.32 10­6 N ∙ m
____________________ [10 points] Maximum number of attempts for credit = 5. (Fraction of credit after that: 0.5 up to 10 attempts)
sp11ex02q04 [10 points] (Last updated: Thu Mar 31 09:28:47 2011) [meiles]
Wire bent in a funny shape Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
When a current is passed through the flexible wire shown in the Figure below, will it tend to bunch up or
form a circle?
Figure 29­48
a. b. c. d. e. Resistivity of the wire is needed to answer this question.
The wire will tend to form a circle.
The wire will tend to bunch up.
The length of the wire is needed to answer this question.
Current in the wire is needed to answer this question.
____________________ [10 points] Maximum number of attempts for credit = 1.
sp11ex02q09 [10 points] (Last updated: Fri Apr 1 08:35:23 2011) [meiles]
Charging a capacitor in a circuit with switch Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
The circuit as shown in the Figure above shows a capacitor C, two ideal batteries, two resistors, and a
switch S. Initially S has been open for a long time. If it is then closed for a long time, by how much does
the charge on the capacitor change? Assume C = 53 F, 1 = 3.4 V, 2 = 0.52 V, R1 = 0.1 , and R2 =
0.71 .
a. b. c. d. e. 133.8 C
1306.98 C
182.11 C
377.66 C
241.82 C
____________________ [10 points] Maximum number of attempts for credit = 1.
sp11ex02q03 [10 points] (Last updated: Thu Apr 7 14:36:37 2011) [meiles]
Capacitor with a dielectric Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
A certain dielectric with a dielectric constant = 24 can withstand an electric field of 4 107 V/m.
Suppose we want to use this dielectric to construct a 0.95 µF capacitor that can withstand a potential
difference of 1830 V. (a) What is the minimum plate separation? (b) What must the area of the plates be?
a. b. c. d. e. (a) 0.046 mm; (b) 1178644 cm2
(a) 0.184 mm; (b) 1178644 cm2
(a) 0.092 mm; (b) 2046 cm2
(a) 0.046 mm; (b) 4092 cm2
(a) 0.046 mm; (b) 2046 cm2
____________________ [10 points] Maximum number of attempts for credit = 1.
sp11ex02q10 [10 points] (Last updated: Thu Mar 31 10:34:38 2011) [meiles]
Combination of electric and magnetic fields Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
An electric field of 1.8 kV/m and a magnetic field of 0.55 T act on a moving electron to produce no net
force. Calculate the minimum speed V of the electron.
a. b. c. d. e. 3.27 103 m/s
0.088 103 m/s
1.07 103 m/s
0.65 103 m/s
12.36 103 m/s
____________________ [10 points] Maximum number of attempts for credit = 1.
sp11ex02q02 [10 points] (Last updated: Thu Mar 31 11:25:22 2011) [meiles]
Multi­loop circuit Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
For the circuit shown above, = 10 V and R = 3 . Find the potential difference between points a and b.
State the magnitude.
a. b. c. d. e. 4 V
13.8 V
6 V
8 V
12 V
____________________ [10 points] Maximum number of attempts for credit = 1. HELP: Using symmetry wisely will save time and effort.
sp11ex02q11 [10 points] (Last updated: Thu Mar 31 09:29:55 2011) [meiles]
LR circuit with a switch and energy source Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
In the circuit shown in the Figure above, = 10 V, R1 = 4.2 , R2 = 9.5 , and L = 4.8 H. For the situation
where the switch S just closed, calculate the current i1 through R1 .
a. b. c. d. e. 2.08 A
2.38 A
1.05 A
0 A
3.43 A
____________________ [10 points] Maximum number of attempts for credit = 1.
sp11ex02q01 [10 points] (Last updated: Wed Mar 30 11:25:05 2011) [meiles]
Battery with internal resistance Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
In the figure above, the emf is 6 V and R = 0.48 . The rate of Joule heating in R is 8 W. What is the value
of r?
a. b. c. d. e. 0.99 5.88 1.95 2.97 0.48 ____________________ [10 points] Maximum number of attempts for credit = 1.
sp11ex02q12 [10 points] (Last updated: Thu Mar 31 09:30:18 2011) [meiles]
Magnetic field on the surface of the wire Don't Forget to Give Answers in Specified Units!
If you have a figure in the present problem do not use the
numbers shown in the figures. Please use the numbers given in the
text of the problem unless you are asked to use the numbers from
the figure!
A 10­gauge bare copper wire (2.6mm in diameter) can carry a current of 50 A without overheating. For this
current what is the magnetic field at the surface of the wire?
a. b. c. d. e. 0
7.69 mT
15.38 mT
30.77 mT
46.15 mT
____________________ [10 points] Maximum number of attempts for credit = 1.
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CHIP ID: meiles
1L Magnetic field of a solenoid is
In[1]:=
Bsol = mu0 * NN  L * i
i mu0 NN
Out[1]=
L
In[2]:=
Out[2]=
Bsol . 8mu0 ® Pi * 4*^-7, NN ® 560, L ® 2.9, i ® 2.5<
0.000606652
2L Torque is defined :
In[9]:=
Out[9]=
torque = p * Bfield * Sin @thetaD
Bfield p Sin @thetaD
the magnetic moment is :
In[11]:=
Out[11]=
p = NN * A * i
A i NN
so :
In[12]:=
Out[12]=
torque . 8NN ® 1000, A ® Pi * 0.0075 ^ 2, i ® 1.4*^-3, Bfield ® 0.25, theta ® Pi  2<
0.0000618501
3L RH rule : magnetic field due to the current at
the location of the current on the opposite side points into the page ;
then the force points out. Thus the force all points out - so it forms a circle .
4L The initial charge is :
In[13]:=
Out[13]=
Qin = c * E2
c E2
The final charge is more complicated . The current only goes around the outer loop :
In[19]:=
current = H E1 - E2L  H R1 + R2L
E1 - E2
Out[19]=
R1 + R2
Now we can calculate the voltage drop across, say , R1 :
In[20]:=
Out[20]=
vdrop = R1 * current
HE1 - E2L R1
R1 + R2
In[24]:=
Out[24]=
so, the voltage across the capacitor is equal to the voltage across
the other side of the parallel circuit : H careful with that minus sign !L
Vcap = E1 - vdrop
E1 -
HE1 - E2L R1
R1 + R2
Now we can calculate the final charge :
In[25]:=
Out[25]=
Qfi = c * Vcap
c
E1 -
HE1 - E2L R1
R1 + R2
Printed by Mathematica for Students
2
examC.nb
In[26]:=
Out[26]=
Qfi - Qin . 8c ® 53*^-6, E1 ® 3.4, E2 ® 0.52, R1 ® 0.1, R2 ® 0.71<
0.000133796
5L Capacitance definition is :
In[27]:=
Capp = e0 * A  d
A e0
Out[27]=
d
Electric field is :
In[28]:=
Efield = V  d
V
Out[28]=
d
So d is :
In[31]:=
Out[31]=
Solve @Efield Š 4*^7, d D . V ® 1830.
88d ® 0.00004575<<
And then the area is :
In[33]:=
Out[33]=
Solve @Capp Š 0.95*^-6, A D . 8d -> 0.00004575`, e0 ® 24 * 8.85*^-12<
88A ® 0.204626<<
Don ' t forget to multiply e0 by K !
6L Forces balance out :
In[34]:=
Out[34]=
In[35]:=
Out[35]=
Solve @q * Ef Š q * v * Bf, v D
:: v ®
Ef
Bf
>>
1.8*^3  0.55
3272.73
7L Homework prob.
8L Inductors - skip !
9L Let ' s put power in terms of current and resistance :
In[43]:=
Out[43]=
P = i^2*R
i2 R
Not only that, but, using Ohm ' s law ,
In[44]:=
i = e Hr + RL
e
Out[44]=
r + R
In[45]:=
Out[45]=
Solve @P Š 8, r D
:: r ®
1
In[46]:=
4
Out[46]=
J
1
-
4
2 e
0.989694
2 e
R - 4 R >, : r ®
1
2 e
4
R - 4 R N . 8e ® 6, R ® 0.48<
R - 4 R >>
Printed by Mathematica for Students
examC.nb
10L Magnetic field of a wire :
In[47]:=
Bfield = mu0 * II  2  Pi  r
II mu0
Out[47]=
2 Π r
In[48]:=
Out[48]=
Bfield . 8mu0 ® Pi * 4*^-7, II ® 50, r ® 0.0026  2<
0.00769231
Printed by Mathematica for Students
3