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W11D3. Magnetic Forces. Reminder. EXAMINATION #3 Wednesday November 9 th. 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!

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### W11D3

Magnetic Forces

Reminder

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.

More

Info Later

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 ARepeat 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.

L

I

Think “BIL”

B out of plane of the paper

We usually calculate force per unit length.

TWO WIRES

Now we can calculate the magnitude of the magnetic force F21exerted on the lower wire by the field produced by the upper wire:

using the right-hand rule with , the direction of the force is up, so that the lower wire is attracted to the upper wire.

B

(B field pointsinto plane of paper.)

v

### Trajectory of Charged Particlesin a Magnetic Field

B

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

v

F

F

Magnetic Force is a centripetal force

Review of Rotational Motion

 = s / r  s =  r  ds/dt = d/dt r  v =  r

s

 = angle,  = angular speed,  = angular acceleration

r

at = r  tangential acceleration

ar = v2 / rradial acceleration

The radial acceleration changes the direction of motion,

while the tangential acceleration changes the speed.

at

ar

Uniform Circular Motion

 = constant  v and ar constant but direction changes

ar

KE = ½ mv2 = ½ mw2r2

ar = v2/r = 2 r

v

F = mar = mv2/r = m2r

### Radius of a Charged ParticleOrbit in a Magnetic Field

Note: as , the magnetic

force does no work!

Centripetal Magnetic

Force Force

=

v

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

F

r

### Cyclotron Frequency

v

B

+ + + +

+ + + +

+ + + +

+ + + +

+ + + +

F

r

The time taken to complete one

orbit is:

V cancels !

### that’s all there is!

Magnetic Forces on Charges