Exam 2 covers Ch. 27-33, Lecture, Discussion, HW, Lab

1
Exam 2 covers Ch. 27-33,Lecture, Discussion, HW,
Lab
Exam 2 is Tue. Oct. 27, 530-7 pm, 145 Birge

• Chapter 27 The Electric Field
• Chapter 29 Electric potential work
• Chapter 30 Electric potential field
• (exclude 30.7)
• Chapter 31 Current Resistance
• Chapter 32 Fundamentals of Circuits
• (exclude 32.8)
• Chapter 33 The Magnetic Field
• (exclude 33.5-33.6, 33.9-10, Hall effect)

2
Law of Biot-Savart
B out of page

• Each short length of current produces
  contribution to magnetic field.

r
?
I in plane of page
ds
3
Vector cross product
Dist. to point at which field is evaluated
Unit vector toward point at which field is
evaluated
Short length of current
4
Field from a circular loop

• Each current element produce dB
• All contributions add as vectors
• Along axis, allcomponents cancelexcept for
  x-comp

5
Magnetic field from loop of current

• Looks like magnetic dipole

6
Building a solenoid
7
Solenoid many current loops
8
Magnetic Force on a Current
I

• Force on each charge
• Force on length of wire

• Force on straight section of wire, length L

N
Current
Magnetic force
Magnetic field
9
Quick Quiz
y

• A current I flows in a square loop of wire with
  side length L.
• A constant B field points in the x-direction,
  perpendicular to the plane of the loop.
• What is the net force on the wire loop?

I
I
I
I

1. 4LB
2. 2LB
3. LB
4. 0

x
10
No force, but torque
Lever arm
Force

• Torque is
• Net torque can be nonzero even when net force is
  zero.

11
Question on torque
Which of these loop orientations has the largest
magnitude torque? Loops are identical apart from
orientation. (A) a (B) b (C) c
a
b
c
12
Quick Quiz

• Which of these different sized current loops has
  the greatest torque from a uniform magnetic field
  to the right? All have same current.

B.
A.
L
2L
W
W/2
L/2
C.
D. All same
2W
13
Torque on current loop
loop area

• Torque proportional to
• Loop area
• Current
• sin?

14
Current loops magnetic dipoles

• Current loop produces magnetic dipole field.
• Magnetic dipole moment

Area of loop
current
direction
magnitude
In a uniform magnetic field
Magnetic field exerts torqueTorque rotates loop
to align with
15
Works for any shape planar loop
perpendicular to loop
Torque in uniform magnetic field
Potential energy of rotation
Lowest energy aligned w/ magnetic field Highest
energy perpendicular to magnetic field
16
Magnetic flux

• Magnetic flux is defined exactly as electric
  flux
• (Component of B ? surface) x (Area element)

zero flux
Maximum flux
SI unit of magnetic flux is the Weber ( 1 T-m2 )
17
Magnetic Flux

• Magnetic flux ? through a surface (component of
  B-field ? surface) X (surface area)
• Proportional to B- field lines penetrating
  surface

18
Why perpendicular component?

• Suppose surface make angle ? surface normal

Component surface
Component ? surface
Only ? componentgoes through surface

• ?B BA cos ?
• ?B 0 if B parallel A
• ?B BA (max) if B ? A
• Flux SI units are Tm2Weber

19
Total flux

• E not constant
• add up small areas where it is constant

• Surface not flat
• add up small areas where it is flat

Add them all up
20
Magnetic flux

• What is that magnetic flux through this surface?

1. Positive
2. Negative
3. Zero

21
Properties of flux lines

• Net magnetic flux through any closed surface is
  always zero

For electric charges, and electric flux
No magnetic charge, so right-hand side0
for mag. Basic magnetic element is the dipole
22
Time-dependent fields

• Up to this point, have discussed only magnetic
  and electric fields constant in time.
• E-fields arise from charges
• B-fields arise from moving charges (currents)

Faradays discovery

• Another source of electric field
• Time-varying magnetic field creates electric field

23
Measuring the induced field

• A changing magnetic flux produces an EMF around
  the closed path.
• How to measure this?
• Use a real loop of wire for the closed path.

The EMF corresponds to a current flow