Transcript Document

Fields
• Model used when force act a distance.
• Quantity / unit measure.
• Direction Too.
Grav field caused by mass
g = Fg/mass.
N/kg
Electric caused by charge
E = Fe/q.
N/C
Magnetic Fields B
• caused by moving charges
• N/C *m/s =
• Tesla T
What is
Magnetism?
Magnetism is the
force of attraction or
repulsion of a
magnetic material
due to the excess
spin of e-.
Can think of e- circling nucleus are
creating bar magnets in magnetic material.
Magnetic Field, B Direction.
Follow compass needle .
Field Strength Strongest near poles. Lines close
together.
Earth’s N geographic pole = S mag pole.
Sketching Fields
Use arrows to show the direction of
compass needle deflection.
Compass needle points
away from N and into S
mag pole.
Symbols
Arrow shows direction in plane of page.
Field into the page X like tail of arrow.
Field out of page … like tip of arrow.
Electric, E & Magnetic, B Fields
Similarities
• Directional Field = vector
• field lines – flux which cannot touch, or bend at
sharp angles, intensity is shown by close
spacing.
• Both attract opposite. Repel like.
• Drop off with distance inverse square.
• Both Polarize objects.
Differences
• Magnet feels no force in static E field.
• Charged particle q, no F in static B field.
• For B field, direction compass needle points.
• For E, field direction + test charge would
move.
Reading Magnetism
Hamper Ch 6.3
• How are magnetic fields sketched?
• How are Electric fields sketched?
• What is the relationship between charges
and magnetic fields?
Moving charges/ currents induce
magnetic fields. In specific directions.
• When a current flows, a magnetic field is
generated.
• *Stationary charges do not generate
magnetic fields, but do cause electric
fields.
Mag Field Direction around Wire.
Field circles perpendicular to wire.
Wire loop – thumb in current direction. Fingers
in B direction.
Solenoid – Loops of wire (can be wrapped
around core of iron).
Solenoids have same field as bar magnets.
And Earth
Hand Rule: Find Mag N pole in solenoid.
Fingers in direction of current, thumb points to
magnetic N. Pole (see field lines).
Charged particles moving in B
fields feel a force!!
Force direction determined by
hand rule three.
Direction of mag force on q perpendicular to velocity
vector & to field.
For +q place right hand fingers into field, thumb points
to v, palm points to mag force.
For –q use left hand or reverse direction of right hand.
Electron in mag field B.
Force is proportional to amount of q on particle.
Magnetic Field Units = Tesla’s
Tesla (T) =
N
C m/s
kg m/s2
Am
N
Am
Strength/Intensity of Mag Field can be
described in terms of force on moving
charge q.
Fmag = qvB sin q
B = Fmag
qv
q = charge
coulombs
v = velocity m/s
F = force Newtons
B = Tesla
The force on the charge only acts perpendicular to
the velocity direction. Charges traveling along
field lines feel no force.
Since arises when the mag field and
velocity are perpendicular:
• Fmag = qvBsinq.
• Where q is the angle between the velocity
and the magnetic field direction.
• When q = zero the force is zero.
• When q = 90 the force is maximum.
Ex 1: A p+ moving east feels a force of 8.8 x
10-19 N upward due to the Earth’s magnetic
field. At this location the field strength is 5.5
x 10-5 T north. Find the speed of the particle.
Fmag = q v B
v = Fmag
qB
8.8 x 10-19 N_
(1.6 x 10-19 C)(5.5 x 10-5 T )
= 100,000 m/s.
If there is a component of velocity parallel to the
field is unaffected. There is a helical effect.
Magnetic Force on q is Fc since it
causes curved motion.
Ex 2: An electron moves at right angles in a
uniform magnetic field of 3.0 x 10-3 T. If its
speed is 3.0 x 105 m/s, what is the radius of
the path of the electron?
• the magnetic force is causing curved
motion so it a centripetal force!
F mag = Fc.
qvB = mv2.
r.
.
r = mv2 = mv.
qvB
qB
5.7 x
-4
10
m.
Force on current carrying wire.
The current in a wire also feels a force in mag
field.
Conventional Current –force direction on wire:
fingers into field, thumb in current direction,
palm points toward force direction.
Force on wire proportional to direction of
field, current, & length of wire in field.
F = BIl sin q
F = force (N)
B = mag field (T)
I = current (A)
l = length of wire (m)
Ex 3: A wire that is carrying a current of
3.5 A east, has 2.00 m of its length in a
uniform field of flux density 5.00 x 10-7T
directed into the paper.
a) Sketch the wire in the field.
b) Find the magnitude and direction
of the force.
F = BIl.
(5.00 x 10-7T )(3.5 A )(2.00 m ) = 3.5 x 10-6 N
up.
Ex 4: A 36-m long wire carries 22 A
current from east to west. If the
maximum magnetic force 4.0 x 10-2 N
directed down, find the magnitude
and direction of the magnetic field at
this location.
F = BIl
B = F/Il.
=
= 5.0 x
4.0x10-2 N.
(22A)(36m)
-5
10
T. north.
The current in the wire must be at right
angles to the field to feel the force so:
F = BIl sin q.
Where q is the angle between the
wire and the field
q
Field & Force Around Parallel
Current Carrying Wires
Since currents generate mag fields,
two parallel wires will each
generate a field that exerts a force
on the adjacent wire. The direction
of the force depends on the current
direction.
Currents in same direction exert attractive forces.
Is this real or conventional current?
Hint hand rule for Force - fingers into the B field created by
the other wire!
Neg current (real).
Current in opposite directions,
create fields with repulsive forces.
By Newton’s 3rd
Law, F2 = -F1.
F1
F2
I1 I2
The Ampere (A) is a unit of rate of
current flow, but is based on the force felt
between 2 current-carrying wires.
The Ampere, not the Coulomb, is
considered a fundamental unit!! Very
weird indeed!
Formal definition of the ampere:
“The constant current which will produce
an attractive force of 2 × 10–7 N/m of length
between two straight, parallel wires of
infinite length and negligible circular cross
section placed one meter apart in a
vacuum".
Mag Field interaction
Between Current Carrying Wires
These show
neg charge
flow.
Do Now: Sketch the E field between parallel plates.
Sketch the path of an electron beam shot into the field.
Crossed Fields
• An e- is shot into the magnetic field as below.
•
a. Sketch its path in the field.
•
b. Suggest a way to use an E field to direct the e- in a
straight line.
•
c. Sketch the electric field that will straighten the e- path.
e-
d. Derive an equation
that expresses the
electric field strength E,
required to keep an e- of
velocity v, moving
through a magnetic field
B, in a straight line.
End Here
No longer in curriculum
For a straight length of wire the mag field can be
expressed as:
B = moI
mo constant find it.
2pr
r = dist fr wire m
I = current - A
B = field strength T
Force between two wires proportional to
current in wires:
F = moI1I2l
2pr
Ex 4: What is the magnitude & direction
of the force btw 5.00 m lengths of wire
each carrying 7.5 A of current in the
same direction if they are separated by
25.0 cm?
2.25 x 10-4 N toward each other.
Mag Field Strength around a solenoid:
B = moNI
l
N = number turns of wire
I = current
l = length of wire in field m
Hwk Sheet.
Do Holt p 782 with IB ref tables
p 781#19, 21, 22, 24, 25, 33, 35, 41, 42