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AMERICAN UNIVERSITY OF SHARJAH
COLLEGE OF ARTS AND SCIENCES
Dept. of Physics
PHY 102 – Fall 2006
Midterm 3 – December 10, 2006
Duration: 50 minutes (Class time)
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Name: _______________________
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ID #: _________________________
Question
Maximum grade
1
10
2
10
3
10
Your grade
1) For the two current carrying wires shown in figure (I1 is out of the page), determine from basic
principles (Ampere’s law or Biot-Savart law) (a) the magnetic field created by each current at point O2 and
(b) the total magnetic field at point O2. (use  = 30o, R1 = 4 cm, R2 = 10 cm I1 = 10 A and I2 = 5 A).
 I dl  rˆ
Biot-Savart Law: dB  0
0  4 107 T  m/A ; Ampere's law :  B  dl  0 I net
2
4 r
loop
To find the magnetic field, B1, created by I1, apply Ampere’s law: Ampere’s loop is a circle of center O1 and
of radius R1/2.
B1  2R1 / 2   0 I net
R12
I net  I 1
 I1 / 4
 ( R1 / 2) 2
 I
B1  0 1  2.5 10 5 T
4R1
The direction of B1 at O2 is to the left
To find the magnetic field, B2, created by I2, apply Biot-Savart law.
Magnetic field at point O2 created by segment “ab” is zero because dl  rˆ  0 .
Magnetic field at point O2 created by segment “cd” is zero because dl  rˆ  0 .
Magnetic field at point O2 created by the arc “bc”: here dl  rˆ  sin(90)dl k  dl k
I
B2   0 22 dl
4 R
I
 I  /6
I
B2  0 22  dl  0 22  Rd  0 2  2.62  106 T (out of page)
0
4 R
4 R
24 R
The total magnetic field at point O2 is B = - 2.5 10 5 T i + 2.62 10 6 T k. The magnitude of this vector is
B  (2.5 10 -5 ) 2  (2.62 10 -6 ) 2  2.5110 -5 T
2) The figure shows a cross section of three parallel wires each carrying a current of 20 A. The currents in
wires A and B are out of the paper, while that in wire C is into the paper. If the distance R = 5 mm, what is
the magnitude of the force on a 2 m length of wire A?
B
R
A
R

C
F  IL  B where L = 2k and B is the total magnetic field created by Ib and Ic at the location of wire A.
 I
B  0 i  j   8 10  4 i  j 
2R
F  3.2 10  2 (i  j )
F  4.53 10  2 N
3) A circular coil (radius = 15 cm) with a total resistance of 4  is placed in a uniform magnetic field
directed perpendicularly to the plane of the coil.
a) If B varies with time according to B = B0 sin (t), where B0 = 80 µT and  = 50 rad/s, calculate the
current induced in the coil at t = 0.020 s?
b) If the coil starts rotating in this varying field B = B0 sin (t), calculate the current induced in the coil at an
instant when the angle between the field and the normal to the plane of the loop is equal to 30° and
increasing at a constant rate of 18°/s.
I

R
d
dt
  BA cos( )
 
In part (a)  = 0, only B changes with time:
dB
  AB0 cos(t )
dt
At t = 0.02 s,   8.9 10 4 V and I = 2.23×10-4A
  A
In part (b) both B and  change with time:
dB
d
   A cos( )  AB
sin( )   AB0 cos(t ) cos( )  AB0  sin(t ) sin( )
dt
dt
Where
d

 18 0 / s  0.1rad / s
dt
  t
The angle between the field and the normal to the plane of the loop is equal to 30° at t   /   30 / 18  1.67 s
 = 3.86 ×10-4 V
I = 9.6 ×10-5 A