ch. 21 - magnetic forces and fields. 3 d- visualization of vectors and current
TRANSCRIPT
Ch. 21 - Magnetic Forces and Fields
3 D- visualization of vectors and current
21.1 Magnetic Fields
The needle of a compass is permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) atthe other.
21.1 Magnetic Fields
The behavior of magneticpoles is similar to that oflike and unlike electric charges.
21.1 Magnetic Fields
Surrounding a magnet there is a magnetic field, an “alteration of space” caused by the magnet. The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point. The variable we use for the magnetic field is B.
21.1 Magnetic Fields
The magnetic field lines and pattern of iron filings in the vicinity of abar magnet and the magnetic field lines in the gap of a horseshoe magnet.
21.1 Magnetic Fields
The iron core of the earth acts as a magnet and the earth has a magneticfield as shown below
21.2 The Force That a Magnetic Field Exerts on a Charge
Recall that when a charge is placed in an electric field, it experiences a force, according to EF
q
The direction of the force is always parallel to or 180° from the direction of the field.
Magnetic Force on a moving charge due to an external magneticB field
• A moving charge is a magnet.
• In the presence of an external magnetic field, the charge will experience a force and change its speed and direction.
• The magnetic field (B) is coming out of the page in this picture.
21.2 The Force That a Magnetic Field Exerts on a Charge
Right Hand Rule No. 1. Extend the right hand so the fingers pointalong the direction of the magnetic field and the thumb points alongthe velocity of the charge. The palm of the hand then faces in the direction of the magnetic force that acts on a positive charge.
If the moving charge is negative,the direction of the force is oppositeto that predicted by RHR-1.
Magnetic Force on a charge moving in a magnetic field (B)
• The magnitude,|Fm|= qvB(sinθ) where θ is the angle between the direction of motion and the direction of B
• The direction of Fm is given by RHR1• The unit of B is the Tesla (Newton/Amp-meter)
F = 0 F<Fmax F = Fmax
tesla10gauss 1 4and is often used when studying the magnetic field of the Earth
Magnetic Force on a moving charge due to an external B field
Fm = qvBsinθ
• Only a moving charge experiences a force.
• There must be a component of velocity perpendicular to the external field, or F = 0.
Magnetic Force on a moving charge due to an external B field
Fm = qvBsinθ
• The force is mutually perpendicular to v and B.
• The force on a negative moving charge is shown by the left hand rule!
Conceptual ProblemA positive charge is
traveling in the direction shown by the arrow. It enters the external B field (dots mean out of the page). The particle experiences a force:
a. to the right
b. to the left
c. into the page
d. out of the page
Conceptual ProblemA positive charge is
traveling in the direction shown by the arrow. It enters the external B field (dots mean out of the page). The particle experiences a force:
a. to the right
b. to the left
c. into the page
d. out of the page
Numerical problem
A particle with a charge of +8.4 μC and a speed of 45 m/s in the direction shown (purple) enters an external magnetic field (red) of 0.30 T. Find the magnitude and the direction of the magnetic force on the particle.
Numerical problemA particle with a charge of +8.4 μC and a speed of 45 m/s in the direction shown(purple) enters an external magnetic field (red) of 0.30 T. Find the magnitude and the direction of the magnetic force on the particle.
Note that vy = v sin 150° is the component perpendicular to the magnetic field.
Answer: 5.67 x 10-5 Newtons, into the page
vy
21.3 The Motion of a Charged Particle in a Magnetic Field
•The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path. •The magnetic force results in a centripetal acceleration. According to Newton’s Law:
r
vmFm
2
r
vmqvB
2
21.4 The Mass Spectrometer
Chemists and biologists use the “mass spec” to identify the the mass and/or charge of molecules.
r
vmqvB
2
21.4 The Mass Spectrometer
The mass spectrum of naturallyoccurring neon, showing threeisotopes.
How much Deuterium in my sample?
Deuterium, (“heavy hydrogen”) has an extra neutron in its nucleus. Researchers want to know the percentage of deuterium in a sample of hydrogen. The hydrogen is ionized and then is accelerated through the metal plates with a potential difference of 2100 V It then enters a uniform B field 0.1T, into the page. Ignore effects due to gravity.
At what radius should the detector be placed?
mp = mn = 1.67 x 10-27 kg
q = e = 1.60 x 10-19 C
We need to use both Conservation of Energy and Newton’s Law for uniform circular motion to solve this problem.
1. find the speed of the particle upon exiting the capacitor, using conservation of energy:
EPE0 = KEf
q ∆V = mv2/2, v = 4.49 x 105 m/s.
2. Use Newton’s Law to find an expression for r:
r = 9.37 x 10-4 m
r
vmqvBFm
2
How much Deuterium in my sample?
Ranking Task3 particles move
perpendicular to a uniform B field and travel in circular paths as shown. They have the same mass and speed. Rank the particles in order of charge magnitude, greatest to least:
a. 3,2,1 c. 2,3,1 b. 3,1,2 d.1,3,2
e. 1,2,3
r
vmqvBFm
2
Ranking Task3 particles move
perpendicular to a uniform B field and travel in circular paths as shown. They have the same mass and speed. Rank the particles in order of charge magnitude, greatest to least:
a. 3,2,1 c. 2,3,1 b. 3,1,2 d.1,3,2
e. 1,2,3
charge and radius are inversely proportional
r
vmqvBFm
2
21.5 The Force on a Current in a Magnetic Field
The magnetic force on themoving charges pushes thewire to the right.
21.5 The Force on a Current in a Magnetic Field
sinqvBF
sinBtvt
qF
L
I
sinILBF
21.6 The Torque on a Current-Carrying Coil
The two forces on the loop have equal magnitude but an applicationof RHR-1 shows that they are opposite in direction.
21.6 The Torque on a Current-Carrying Coil
The loop tends to rotate such that itsnormal becomes aligned with the magneticfield.
21.6 The Torque on a Current-Carrying Coil
sinsinsinNet torque 21
21 IABwILBwILB
sin
momentmagnetic
BNIA
number of turns of wire
What happens to the loop?The magnetic field
exerts:a. a net force and a net
torqueb. a net force but no net
torquec. a net torque, but no
net forced. neither a net force,
nor a net torque
What happens to the loop?The magnetic field
exerts:a. a net force and a net
torqueb. a net force but no net
torquec. a net torque, but no
net forced. neither a net force,
nor a net torque
What happens to this loop?
B = 0.25T, I = 12 A
Single turn square with sides of 0.32m length
Part 1: Is there a torque?
a. yes, top out of the page, bottom into the page
b. yes, left side out of the page, right side into the page
c. no torque
What happens to this loop?
B = 0.25T, I = 12 A
Single turn square with sides of 0.32m length
Part 1: Is there a torque?
a. yes, top out of the page, bottom into the page
b. yes, left side out of the page, right side into the page
c. no torque
What happens to this loop?
B = 0.25T, I = 12 A
Single turn square with sides of 0.32m length
Part 2: What is the magnitude of the torque?
What happens to this loop?
B = 0.25T, I = 12 A
Single turn square with sides of 0.32m length
Part 2: What is the magnitude of the torque?
= F(L/2)top + F(L/2)bottom Or
= NIAB
= 30.7 N-m
21.6 The Torque on a Current-Carrying Coil
Example 6 The Torque Exerted on a Current-Carrying Coil
A coil of wire has an area of 2.0x10-4m2, consists of 100 loops or turns,and contains a current of 0.045 A. The coil is placed in a uniform magneticfield of magnitude 0.15 T. (a) Determine the magnetic moment of the coil.(b)Find the maximum torque that the magnetic field can exert on the coil.
(a)
2424
momentmagnetic
mA100.9m100.2A 045.0100 NIA
mN104.190sinT 15.0mA100.9sin 424
momentmagnetic
BNIA(b)
21.6 The Torque on a Current-Carrying Coil
The basic components of a dc motor.
21.6 The Torque on a Current-Carrying Coil
21.7 Magnetic Fields Produced by Currents
Right-Hand Rule No. 2. Curl the fingers of theright hand into the shape of a half-circle. Point the thumb in the direction of the conventional current, and the tips of the fingers will pointin the direction of the magnetic field.
21.7 Magnetic Fields Produced by Currents
A LONG, STRAIGHT WIRE
r
IB o
2
AmT104 7 o
permeability of free space
21.7 Magnetic Fields Produced by Currents
Example 7 A Current Exerts a Magnetic Force on a Moving Charge
The long straight wire carries a currentof 3.0 A. A particle has a charge of +6.5x10-6 C and is moving parallel tothe wire at a distance of 0.050 m. Thespeed of the particle is 280 m/s.
Determine the magnitude and direction of the magnetic force on the particle.
21.7 Magnetic Fields Produced by Currents
sin2
sin
r
IqvqvBF o
r
IB o
2
21.7 Magnetic Fields Produced by Currents
Current carrying wires can exert forces on each other.
21.7 Magnetic Fields Produced by Currents
Conceptual Example 9 The Net Force That a Current-Carrying WireExerts on a Current Carrying Coil
Is the coil attracted to, or repelled by the wire?
21.7 Magnetic Fields Produced by Currents
A LOOP OF WIRE
center of circular loop
R
IB o
2
21.7 Magnetic Fields Produced by Currents
Example 10 Finding the Net Magnetic Field
A long straight wire carries a current of 8.0 A and a circular loop ofwire carries a current of 2.0 A and has a radius of 0.030 m. Find themagnitude and direction of the magnetic field at the center of the loop.
21.7 Magnetic Fields Produced by Currents
R
I
r
I
R
I
r
IB ooo 2121
222
T101.1
m 030.0
A 0.2
m 030.0
A 0.8
2
AmT104 57
B
21.7 Magnetic Fields Produced by Currents
The field lines around the bar magnet resemble those around the loop.
21.7 Magnetic Fields Produced by Currents
21.7 Magnetic Fields Produced by Currents
A SOLENOID
Interior of a solenoid nIB o
number of turns perunit length
21.7 Magnetic Fields Produced by Currents
A cathode ray tube.
21.8 Ampere’s Law
AMPERE’S LAW FOR STATIC MAGNETIC FIELDS
For any current geometry that produces a magnetic field that does not change in time,
IB o ||
net currentpassing throughsurface bounded by path
21.8 Ampere’s Law
Example 11 An Infinitely Long, Straight, Current-Carrying Wire
Use Ampere’s law to obtain the magnetic field.
IB o ||
IB o
IrB o 2
r
IB o
2
21.9 Magnetic Materials
The intrinsic “spin” and orbital motion of electrons gives rise to the magnetic properties of materials.
In ferromagnetic materials groups of neighboring atoms, forming magnetic domains, the spins of electrons are naturally aligned witheach other.
21.9 Magnetic Materials
21.9 Magnetic Materials