Download Document

Chapter 29
Magnetic Fields
Dr. Jie Zou
PHY 1361
1
Outline


Magnetic fields (29.1)
Magnetic force on a charged particle moving
in a magnetic field (29.1)



Magnitude
Direction: right-hand rule
Magnetic force on a current-carrying
conductor (29.2)



Straight wire
Curved wire
Wire loop
Dr. Jie Zou
PHY 1361
2
Magnetic fields
A spoon-shaped
compass
Dr. Jie Zou
Lifting fingerprints by
a magnetic brush
PHY 1361
Magnetic field lines
3
Magnetic force on a charged particle
moving in a magnetic field

Vector expression for the magnetic
force on a charged particle moving in
a magnetic field: FB = qv  B






SI unit of B: the tesla (T); 1 T = 1
N/(C·m/s)

Dr. Jie Zou
Magnitude of the magnetic force
FB = |q|vB sin 
If  = 0 or 180, v // B, FB = 0.
If  = 90, v  B, FB is maximum.
If v = 0, non-moving charge, FB = 0.
Direction of the magnetic force? – use the
right-hand rule.
Another unit in common use: gauss (G);
1 T = 104 G.
PHY 1361
4
Right-hand rule


FB is  to both v and B; FB is  to the
plane formed by v and B.
To find the direction of FB = qv  B:



Dr. Jie Zou
(1) Find the direction of the cross product
v  B, using the right-hand rule.
Right-hand rule: Point the four fingers
of your right hand along the direction of v
and curl them toward B. The extended
thumb points in the direction of v  B.
(2) If q is “+”, FB is in the direction of
your thumb; if q is “-”, FB is opposite the
direction of your thumb.
PHY 1361
5
Quick Quiz

An electron moves in the plane of this paper
toward the top of the page. A magnetic field
is also in the plane of the page and directed
toward the right. The direction of the
magnetic force on the electron is

(a) toward the top of the page, (b) toward the
bottom of the page, (c) toward the left edge of
the page, (d) toward the right edge of the page,
(e) upward out of the page, (f) downward into the
page.
Dr. Jie Zou
PHY 1361
6
Example 29.1 An electron
moving in a magnetic field

An electron in a television picture tube
moves toward the front of the tube with
a speed of 8.0 x 106 m/s along the x
axis. Surrounding the neck of the tube
are coils of wire that create a magnetic
field of magnitude 0.025 T, directed at an
angle of 60 to the x axis and lying in the
xy plane. Calculate the magnetic force on
the electron. Find both the magnitude
and direction of the force.


Dr. Jie Zou
(A) Use equation FB = qv  B.
(B) Use a vector expression.
PHY 1361
7
Important differences between
eclectic and magnetic forces



The electric force acts along the direction of the
electric field, whereas the magnetic force acts
perpendicular to the magnetic field.
The electric force acts on a charged particle
regardless of whether the particle is moving, whereas
the magnetic force acts on a charged particle only
when the particle is in motion.
The electric force does work in displacing a charged
particle, whereas the magnetic force associated with
a steady magnetic field does no work when a particle
is displaced because the force is perpendicular to the
displacement.
Dr. Jie Zou
PHY 1361
8
Magnetic force acting on a
current-carrying conductor

Magnetic force on a straight
segment of current-carrying
wire in a uniform magnetic
field: FB = I L  B.

Straight wire

L: a vector; direction along I;
magnitude equals to L.
Magnetic force on a curved
current-carrying wire in a
uniform magnetic field:
b
FB  I   ds   B  IL  B
 a 

Curved wire
Dr. Jie Zou
Closed current loop
Net magnetic force acting on
any closed current loop in a
uniform magnetic field:
PHY 1361
 
FB  I  ds  B  0
9
An example
Dr. Jie Zou
PHY 1361
10
Quick Quiz

Dr. Jie Zou
Rank the wires
according to the
magnitude of the
magnetic force
exerted on them.
PHY 1361
11
Example 29.2 Force on a
semicircular conductor

Dr. Jie Zou
A wire bent into a semicircle
of radius R forms a closed
circuit and carries a current I.
The wire lies in the xy plane,
and a uniform magnetic field
is directed along the positive
y axis. Find the magnetic
force acting on the straight
portion of the wire and on
the curved portion.
PHY 1361
12