### Slides on Circular Motion

```W11D3
Magnetic Forces
EXAMINATION #3
Wednesday
November 9th
Calendar Thing

Today (Watch for last WA before exam. Sorry about
the intensity of these!)
Quiz
 Who wants to present their experimental results?


Collected now!
Some Problems (No Evan Show! He is cutting class today))
 Continue with Forces


Next Week
Monday - As much of remainder of chapter as possible.
Nothing DIFFICULT from this session will be on exam.
 Wednesday Exam


Second Hour & Friday … moving along!
FINAL EXAMINATION








Monday morning – December 3rd 7:30AM
Physical Science Building
First Floor Conference Room
Location is SECRET!!
TWO index cards allowed
Calculator
Writing Instrument
YOU.
In the circuit shown below, the emf of the battery is 7.6 volts. Resistor R1
has a resistance of 33 ohms, resistor R2 has a resistance of 47 ohms,
and resistor R3 has a resistance of 57 ohms. A steady current flows
through the circuit.
a) What is the equivalent resistance of R1 and R2?
(b) What is the equivalent resistance of all the resistors: R1, R2, and R3
(c) What is the conventional current through R3?
Switch S in the figure below is closed at time t = 0, to begin charging an initially
uncharged capacitor of capacitance C = 10.0 µF through a resistor of resistance R
= 16.0 W At what time is the electric potential across the capacitor equal to that
across the resistor? t = 0.111 ms
.
In the circuit of the figure below, = 2.0 kV, C = 5.5 µF, R1 = R2 = R3 = 0.63 MΩ. With C
completely uncharged, switch S is suddenly closed (at t = 0).
a) At t = 0, what is current i1 in resistor 1? 0.00212 A
(b) At t = 0, what is current i2 in resistor 2? 0.00106 A
(c) At t = 0, what is current i3 in resistor 3? 0.00106 A
Repeat for t = infinity (that is, after many time
constants.)
(d) What is current i1? 0.00159 A
(e) What is current i2? 0.00159 A
(f) What is current i3? 0 A
(g) What is the potential difference V2 across resistor 2
at t = 0? 667 V
(h) What is V2 at t =
?
1000 V
(i) Sketch V2 versus t between these two extreme times.
(Do this on paper. Your instructor may ask you to turn in
this sketch.)
In the figure below, the battery has a potential difference of 10.0 V and the
five capacitors each have a capacitance of 16.0 µF.
(a) What is the charge on capacitor 1? 0.00016 C
(b) What is the charge on capacitor 2? 3.2e-05 C
MORE ON FORCES
Remember Bil?
Bil
FORCES BETWEEN WIRES
Opposites don’t always attract!
The Wire in More Detail – Conventional
Assume all electrons are moving
with the same velocity vd.
q  I t  I
I
L
L
vd
F  qv d B  I
L
vd
v d B  IL B
vector :
F  IL  B
Think “BIL”
V ector L in the direction of the
m otion of P O S IT IV E charge (I).
B out of plane of the paper
TWO WIRES
B 
0 2I
4
r
TWO WIRES
Now we can calculate the magnitude of the magnetic force F21 exerted on the lower
wire by the field produced by the upper wire:
F2 1  I 2 L
using the right-hand rule with
IΔL × B
lower wire is attracted to the upper wire.
 0 2 I1
4
d
B
, the direction of the force is up, so that the
Let’s Get Dizzy!
Trajectory of Charged Particles
in a Magnetic Field
(B field points into plane of paper.)
+
+B
+
v+
+
+
+
+
+
+
+
+ F
+
+
+
+ F +
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
B
+
+
+
+
+
v
Magnetic Force is a centripetal force
Review of Rotational Motion

 = s / r  s =  r  ds/dt = d/dt r  v =  r
s
r
 = angle,  = angular speed,  = angular acceleration

at
ar
at = r 
tangential acceleration
ar = v2 / r radial acceleration
The radial acceleration changes the direction of motion,
while the tangential acceleration changes the speed.
Uniform Circular Motion
ar
16
 = constant  v and ar constant but direction changes

v
ar = v2/r = 2 r
KE = ½ mv2 = ½ mw2r2
F = mar = mv2/r = m2r
Radius of a Charged Particle
Orbit in a Magnetic Field
+B
+
v+
+
+
+
+
+
F
+
+
+
+
+
r
+
+
+
+
+
+
Centripetal
Force

mv
=
Magnetic
Force
2
 qvB
r
+

r 
mv
qB
 
Note: as F  v , the magnetic
force does no work!
Cyclotron Frequency
+B
+
+
v+
+
+
+
+
F
+
+
+
+
+
+
+
r
+
+
+
+
+
The time taken to complete one
orbit is:
T 
2 r
v

2
mv
v
qB
f 
1
T

qB
2 m
 c  2 f 
qB
m
More Circular Type Motion in a
Magnetic Field
19
Magnetic Sector - Mass Spectrometer
20
Velocity
Selector
r
mv
qB
How Old is That?? Activity
SIMS
THAT’S ALL THERE IS!
Magnetic Forces on Charges
```