Magnets and Currents

1
Magnets and Currents
2
Objectives

• Determine the force on an electric charge in a
  magnetic field.
• Explain the electric potential created by a
  changing magnetic field.

3
Vector Direction Conventions
4
CPS Question

• What is the direction of the cross product A ? B?

A
B
5
Cross Product Review
a
A
q
B
b
?A?B? area of parallelogram
6
Cross Product Review

• Curl right-hand fingers in direction of q
• Right-hand thumb points in direction of
  cross-product
• Not commutative

7
Lorentz Force Direction
qv
Source Griffith, The Physics of Everyday
Phenomena
Right-Hand Rule
8
Magnetic Force on a Charge

• F 0 unless charge is moving
• F 0 if velocity is ?? to field
• F maximum if velocity is ? to field
• F ? 0 only if charge crosses B field lines

9
Make an Origami Right Hand
fold over
10
Group CPS Question

• What is the direction of the force on the object
  moving with velocity v through magnetic field B?

A.
D.

B.
E.
C.
F.
11
Group CPS Question

• What is the magnitude of the force on object A
  compared to the magnitude of the force on object
  B?

• FB 4 FA
• FB 2 FA
• FB FA
• FB FA/2
• FB FA/4

A
B
12
Group CPS Question

• How does the work done on object A compare to the
  work done on object B?

A
B

• wB gt wA.
• wB wA.
• wB lt wA.

13
Group Work

• Show that the SI unit of magnetic field B is

This unit is called the tesla T.
14
Group Work

• A current runs through one wire of a pair of
  parallel wires. What is the direction of the
  resulting magnetic field at the location of the
  other wire?

I
?
15
Force between parallel currents
What is the force on this current?I ? B
16
Group CPS Question

• Two parallel wires carrying currents in the same
  direction

• attract each other.
• repel each other.
• have no effect on each other.

Think of their magnetic fields and charge
movements!
17
Definition of Ampere

• If two parallel wires are held 1 m apart,
• with currents of 1 A through each wire,
• the attractive force between the wires is
  2 ? 107 N for each meter of length of the wires.

18
Magnetic Induction

• Transforming energy with magnetism

19
Lorentz Force Reminder
Source Griffith, The Physics of Everyday
Phenomena
F is directed out of the screen.
20
CPS Question

• What is the direction of the Lorentz force on the
  charges moving in this wire?

B
A.
D.
B.
E.
C.
F.
I
21
Current in a Field Feels a Force
B
F
I
22
Loop in a Field Has Torque
B
I
I
23
Torque Turns a Motor
24
Moving Creates a Potential
B
v
25
Rotating Loop Creates Circuit
B
26
Rotating Loop Creates Circuit
B
V
V
27
Rotation Powers a Generator
which generates a current
that charges the battery
28
Magnetic Flux

• Field through a surface
• F BA
• Effectively the number of field lines through a
  loop

29
Magnetic Flux

• Greatest flux at a, c, e
• Zero flux at b, d

30
Flux Change Creates Potential

• Faradays Law

Changing the magnetic flux through a loop creates
an electric potential around the loop.
B field A area F BA
31
Faradays Law

• Greatest flux F when perpendicular (a, c, e)
• Fastest change in flux DF/Dt when parallel (b, d)

32
Induced current direction

• Lenzs Law

The current induced by changing the magnetic flux
inside a circuit generates a magnetic field that
opposes the change.
33
Lenzs Law Explains Generator
34
Group Work
What is the Lorentz force on each side? Which
direction is the flux change? What current would
oppose it?
B

• If the loop inside this magnetic field expands,
  in what direction will the induced current be?

35
How a Microphone Works

• microphone
• geophone

36
How a Loudspeaker Works

• loudspeaker

induced motion of magnet
current-generated field attracts or repels magnet
current