Magnetic Flux Density

1
Magnetic Flux Density

• Magnetic flux lines are continuous and closed.

• Direction is that of the B vector at any point.

• Flux lines are NOT in direction of force but .

When area A is perpendicular to flux
The unit of flux density is the Weber per square
meter.
2
Calculating Flux Density When Area is Not
Perpendicular
The flux penetrating the area A when the normal
vector n makes an angle of q with the B-field is
The angle q is the complement of the angle a that
the plane of the area makes with the B field.
(Cos q Sin a)
3
Origin of Magnetic Fields
Recall that the strength of an electric field E
was defined as the electric force per unit charge.
Since no isolated magnetic pole has ever been
found, we cant define the magnetic field B in
terms of the magnetic force per unit north pole.
We will see instead that magnetic fields result
from charges in motionnot from stationary charge
or poles. This fact will be covered later.
4
Magnetic Force on Moving Charge
Imagine a tube that projects charge q with
velocity v into perpendicular B field.
Upward magnetic force F on charge moving in B
field.
Each of the following results in a greater
magnetic force F an increase in velocity v, an
increase in charge q, and a larger magnetic field
B.
5
Direction of Magnetic Force
The force is greatest when the velocity v is
perpendicular to the B field. The deflection
decreases to zero for parallel motion.
6
Force and Angle of Path
Deflection force greatest when path perpendicular
to field. Least at parallel.
7
Definition of B-field
Experimental observations show the following
By choosing appropriate units for the constant of
proportionality, we can now define the B-field as
A magnetic field intensity of one tesla (T)
exists in a region of space where a charge of one
coulomb (C) moving at 1 m/s perpendicular to the
B-field will experience a force of one newton (N).
8
Example 1. A 2-nC charge is projected with
velocity 5 x 104 m/s at an angle of 300 with a
3 mT magnetic field as shown. What are the
magnitude and direction of the resulting force?
Draw a rough sketch.
q 2 x 10-9 C v 5 x 104 m/s B 3 x 10-3 T
q 300
Using right-hand rule, the force is seen to be
upward.
Resultant Magnetic Force F 1.50 x 10-7 N,
upward
9
Forces on Negative Charges
Forces on negative charges are opposite to those
on positive charges. The force on the negative
charge requires a left-hand rule to show downward
force F.
10
Indicating Direction of B-fields
One way of indicating the directions of fields
perpen-dicular to a plane is to use crosses X and
dots
11
Practice With Directions
What is the direction of the force F on the
charge in each of the examples described below?
negative q
12
Crossed E and B Fields
The motion of charged particles, such as
electrons, can be controlled by combined electric
and magnetic fields.
Note FE on electron is upward and opposite
E-field.
But, FB on electron is down (left-hand rule).
Zero deflection when FB FE
13
The Velocity Selector
This device uses crossed fields to select only
those velocities for which FB FE. (Verify
directions for q)
When FB FE
By adjusting the E and/or B-fields, a person can
select only those ions with the desired velocity.
14
Example 2. A lithium ion, q 1.6 x 10-16 C, is
projected through a velocity selector where B
20 mT. The E-field is adjusted to select a
velocity of 1.5 x 106 m/s. What is the electric
field E?
E vB
E 3.00 x 104 V/m
E (1.5 x 106 m/s)(20 x 10-3 T)
15
Circular Motion in B-field
The magnetic force F on a moving charge is always
perpendicular to its velocity v. Thus, a charge
moving in a B-field will experience a centripetal
force.
Centripetal Fc FB
The radius of path is
16
Mass Spectrometer
Ions passed through a velocity selector at known
velocity emerge into a magnetic field as shown.
The radius is
The mass is found by measuring the radius R
17
Example 3. A Neon ion, q 1.6 x 10-19 C, follows
a path of radius 7.28 cm. Upper and lower B 0.5
T and E 1000 V/m. What is its mass?
v 2000 m/s
m 2.91 x 10-24 kg
18
Summary
The direction of forces on a charge moving in an
electric field can be determined by the
right-hand rule for positive charges and by the
left-hand rule for negative charges.
19
Summary (Continued)
For a charge moving in a B-field, the magnitude
of the force is given by
F qvB sin q
20
Summary (Continued)
The velocity selector
The mass spectrometer