Physics
ys cs 132:
3 Lecture
ectu e 18
8
Elements of Physics II
A
Agenda
d for
f T
Today
d



Magnets and the Magnetic Field
Magnetic fields caused by charged particles
 B-field from a current-carrying wire
Magnetic fields
f
and forces
f
 B-fields
 Magnetic forces on moving particles
Physics 201: Lecture 1, Pg 1
Example:
In the following figure, what is the value of the
potential at points a and b?
Physics 201: Lecture 1, Pg 2
Magnets and Magnetic Forces

Magnet: An object consisting of two poles called
North and South
 Poles of a magnet are the ends where objects are most
strongly attracted

Magnets will apply a force on other magnets
 Like p
poles repel
p each other and unlike p
poles attract each
other

Magnetic poles cannot be isolated
 If a permanent magnetic is cut in half repeatedly
repeatedly, you
will still have a north and a south pole
 This differs from electric charges
 There is some theoretical basis for monopoles
monopoles, but none
have been detected
Physics 201: Lecture 1, Pg 3
Magnetism
Physics 201: Lecture 1,Slide
Pg 4 24-12
B-field

Similar to electric charges a magnet will create a
magnetic field in the area around it

Due to convention we will call the magnetic field
a B-field

The force magnets apply on each other can be
described as an interaction between a magnet
and another magnet’s B-field
Physics 201: Lecture 1, Pg 5
B-field lines

We will also draw magnetic field lines

( ) The
(1)
ed
direction
ec o o
of a magnetic
ag e c field
e d is
s tangent
a ge to
o
a magnetic field line at any point

(2) The number of lines per area is proportional
to the magnitude of the B-field
Physics 201: Lecture 1, Pg 6
Mapping Magnetic Field
Physics 201: Lecture 1, Pg 7
B-Field Lines
Physics 201: Lecture 1, Pg 8
Field Lines of Bar Magnet
S
N
Magnetic field lines don’t start or
stop.
stop
There are no magnetic charges
(monopoles)
Physics 201: Lecture 1, Pg 9
Clicker Question 1:
Physics 201: Lecture 1, Pg 10
B-field of Current-Carrying Wire

In 1819 Hans Christian Oersted discovered that
an electric current in a wire causes a compass to
turn.
Physics 201: Lecture 1, Pg 11
Notation


Magnetism requires a three-dimensional
perspective, but two-dimensional figures are
easier
i tto draw.
d
We will use the following notation:
Physics 201: Lecture 1, Pg 12
B Field from wire
B-Field
Magnetic field lines are
imaginary lines drawn
through a region of space
so that:
th t
 A tangent to a field line is in
the direction of the magnetic
field.
 The field lines are closer
t
together
th where
h
the
th
magnetic field strength is
larger.
Physics 201: Lecture 1, Pg 13
RHR
Physics 201: Lecture 1, Pg 14
The Source of the Magnetic Field: Moving
Charges

The magnetic field of a charged
particle q moving with velocity v
is given by the Biot-Savart law:
Physics 201: Lecture 1, Pg 15
The Magnetic Field
The constant 0 in the Biot-Savart law is called the
permeability constant:
0 = 4 × 10-7 T m/A = 1.257 × 10-6 T m/A
The SI unit of magnetic
g
field strength is the
tesla, abbreviated as T:
1 tesla = 1 T = 1 N/A m
Physics 201: Lecture 1, Pg 16
Magnetic Field of a Moving Positive Charge


The right-hand
right hand rule for finding
the direction of B-field due to a
moving
gp
positive charge
g is
similar to the rule used for a
current carrying wire.
N t th
Note
thatt the
th componentt off
parallel to the line of motion is
zero.
Physics 201: Lecture 1, Pg 17
Currents Create B-Fields
Magnitude:
 0I
B
2r
Current I OUT
B
0  4   10 77 Tm / A
r
•
r = distance from wire
Direction of B-field from current
carrying wire:
Curly right hand rule
Lines of B
Thumb along current I,
direction of B along curled fingers
fingers.
Physics 201: Lecture 1, Pg 18
Clicker Question 2:
What is the current direction in the wire of the figure?
A.
B.
Upward.
Downward.
Physics 201: Lecture 1, Pg 19
Clicker Question 3:
A long, straight wire extends into and out of the screen.
The current in the wire is
A.
B.
C.
D.
Into the screen.
Out of the screen.
Th
There
i no currentt iin th
is
the wire.
i
Not enough info to tell the direction.
Physics 201: Lecture 1, Pg 20
Clicker Question 4:
What is the direction of the magnetic field at the
position of the dot?
A.
A
B.
C
C.
D.
E
E.
Into the screen.
screen
Out of the screen.
Up
Up.
Down.
Left
Left.
-
Physics 201: Lecture 1, Pg 21
Clicker Question 5:
The wires are located at ((-2,0)
2 0) meters and (2
(2,0)
0)
meters. The former carries 3 A coming out from the
sheet of the paper, and the latter 3 A going into it.
What is By, the y component of the magnetic field at
the origin?
(a) By = -6
6 × 10-7 T
(b) By = -3 × 10-7 T
(c) By = 0 T
(d) By = +3 × 10-7 T
(e) By = +6 × 10-7 T
Physics 201: Lecture 1, Pg 22
Clicker Question 6:
Two long wires carry equal but opposite current.
What is the direction of the magnetic field above
and midway between the two wires carrying
current (point x)?
X
A.
B
B.
C.
D.
E
E.
Left
Right
Up
Down
Z
Zero
x
Physics 201: Lecture 1, Pg 23
Clicker Question 7:

A current
current-carrying
carrying wire passes through a uniform
external magnetic field, as shown above. (c)
At which point is the total magnetic field the
strongest?
(a)
(b)
(c)
(d)
(e)
A
B
C
D
The total magnetic field strength is uniform
throughout.
Physics 201: Lecture 1, Pg 24
Clicker Question 8:
The magnetic field at point P is zero. What are the magnitude
and direction off the current in the lower wire?
?
A.
B.
C.
D.
E.
10 A to the right.
5 A to the right.
2.5 A to the right.
10 A to the left.
5 A to the left.
Physics 201: Lecture 1, Pg 25
Clicker Question 9:


A squa
square
e loop
oop o
of wire
e ca
carries
es a cu
current
e I. Cu
Current
e is
s
flowing in a counterclockwise direction as shown.
What is the direction of the magnetic field at A?
(a) into the page
(b) out of the page
(c) the B-field is zero
Physics 201: Lecture 1, Pg 26