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.


The behavior of magneticpoles is similar to that oflike and unlike electric charges.


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.


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.


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

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

http://en.wikipedia.org/wiki/File:Ms_block_schematic.gif

http://en.wikipedia.org/wiki/File:Ms_block_schematic.gif

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.


The loop tends to rotate such that itsnormal becomes aligned with the magneticfield.


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 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


B = 0.25T, I = 12 A


Part 2: What is the magnitude of the torque?


B = 0.25T, I = 12 A


Part 2: What is the magnitude of the torque?

= F(L/2)top + F(L/2)bottom Or

= NIAB

= 30.7 N-m


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)


The basic components of a dc motor.

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.


A LONG, STRAIGHT WIRE

r

IB o

2

AmT104 7 o

permeability of free space


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.


sin2

sin

r

IqvqvBF o

r

IB o

2


Current carrying wires can exert forces on each other.


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?


A LOOP OF WIRE

center of circular loop

R

IB o

2


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.


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


The field lines around the bar magnet resemble those around the loop.


A SOLENOID

Interior of a solenoid nIB o

number of turns perunit length


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

Ch. 21 - Magnetic Forces and Fields

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