AP Physics B - Magnetic Fields and Forces

7/22/2019 AP Physics B - Magnetic Fields and Forces

1/21

Magnetic Fields and Forces

AP Physics B


2/21

Facts about Magnetism Magnets have 2 poles

(north and south)

Like poles repel

Unlike poles attract

Magnets create aMAGNETIC FIELDaround them


3/21

Magnetic FieldA bar magnet has a magnetic field

around it. This field is 3D in natureand often represented by lines

LEAVING north and ENTERINGsouth

To define a magnetic field you need

to understand the MAGNITUDEand DIRECTION

We sometimes call the magnetic fielda B-Field as the letter B is theSYMBOL for a magnetic field withthe TESLA (T) as the unit.


4/21

Magnetic Force on a moving chargeIf a MOVING CHARGEmoves into a magneticfield it will experience aMAGNETIC FORCE.This deflection is 3D innature.

N

N

S

S

-

vo

B

sinqvBF

BvqF

B

B

=

=r

r

r The conditions for the force are:

Must have a magnetic field presentCharge must be movingCharge must be positive or negative

Charge must be movingPERPENDICULAR to the field.


5/21

ExampleA proton moves with a speed of 1.0x105 m/s through the Earths magnetic field,which has a value of 55T at a particular location. When the proton moveseastward, the magnetic force is a maximum, and when it moves northward, nomagnetic force acts upon it. What is the magnitude and direction of the magnetic

force acting on the proton?

==

===

B

B

B

F

xxxF

qvBF

)1055)(100.1)(106.1(

190sin,90,

6519

8.8x10-19 N

The direction cannot be determined precisely by the given information. Since

no force acts on the proton when it moves northward (meaning the angle isequal to ZERO), we can infer that the magnetic field must either go northwardor southward.


6/21

Direction of the magnetic force?

Right Hand Rule To determine the DIRECTION of theforce on a POSITIVE charge weuse a special technique that

helps us understand the3D/perpendicular nature ofmagnetic fields.

Basically you hold your right

hand flat with your thumbperpendicular to the rest of your

fingers

The Fingers = Direction B-Field

The Thumb = Direction of velocityThe Palm = Direction of the Force

For NEGATIVE charges use left hand!


7/21

ExampleDetermine the direction of the unknown variable for a protonmoving in the field using the coordinate axis given

+y

+x+z

B = -xv = +yF =+z

B =+Z

v = +xF =-y

B = -zv = +yF =-x


8/21

ExampleDetermine the direction of the unknown variablefor an electron using the coordinate axis given.

+y

+x+z

B = +xv = +yF =+z

B =v = - xF = +y

-z

F

B

B = +z

v =F = +y+x


9/21

Magnetic Force and Circular MotionX X X X X X X X X

X X X X X X X X X

X X X X X X X X X

X X X X X X X X X

vB

- -

FB

FB

FB

FB -

-

-

Suppose we have an electron

traveling at a velocity , v, entering

a magnetic field, B, directed into

the page. What happens after theinitial force acts on the charge?


10/21

Magnetic Force and Circular MotionThe magnetic force is equal to the

centripetal force and thus can be usedto solve for the circular path. Or, if the

radius is known, could be used tosolve for the MASS of the ion. This

could be used to determine the

material of the object.

There are many other types of

forces that can be set equal to themagnetic force.


11/21

Example

?

5.0

250

105.2

106.1

26

19

=

=

=

=

=

r

TB

VV

kgxm

Cxq

qB

mvr

r

mvqvBFF cB ===

2

==

=

=

==

26

19

2

105.2

)106.1)(250(22

21

x

x

m

Vqv

q

mv

q

K

q

WV

A singly charged positive ion has a mass of 2.5 x 10-26kg. After being

accelerated through a potential difference of 250 V, the ion enters amagnetic field of 0.5 T, in a direction perpendicular to the field.

Calculate the radius of the path of the ion in the field.

We need to

solve for thevelocity!

56,568 m/s

==

)5.0)(106.1(

)568,56)(105.2(19

26

x

xr 0.0177 m


12/21

Mass SpectrometersMass spectrometry is an analytical technique that identifies thechemical composition of a compound or sample based on themass-to-charge ratio of charged particles. A sample undergoeschemical fragmentation, thereby forming charged particles (ions).The ratio of charge to mass of the particles is calculated bypassing them through ELECTRIC and MAGNETIC fields in amass spectrometer.


13/21

M.S. Area 1 The Velocity Selector

BEvvBE

qEqvBFF EB

==

==When you inject the sample you want it

to go STRAIGHT through the plates.Since you have an electric field youalso need a magnetic field to apply a

force in such a way as to CANCEL outthe electric force caused by the electric

field.


14/21

M.S. Area 2 Detector RegionAfter leaving region 1 in a straight line, it

enters region 2, which ONLY has a magneticfield. This field causes the ion to move in a

circle separating the ions separate by mass.This is also where the charge to mass ratiocan then by calculated. From that point,

analyzing the data can lead to identifyingunknown samples.

r

Bv

m

q

r

mvqvBFF cB

=

==2


15/21

Charges moving in a wire

Up to this point we have focused our attention onPARTICLES or CHARGES only. The charges couldbe moving together in a wire. Thus, if the wire had aCURRENT (moving charges), it too will experience aforce when placed in a magnetic field.

You simply used the RIGHT

HAND ONLY and the thumb

will represent the direction ofthe CURRENT instead of thevelocity.


16/21

Charges moving in a wire

sin

sin))((

sin

ILBF

Bvtt

qF

t

tqvBF

B

B

B

=

=

=

At this point it is VERY important that

you understand that the MAGNETICFIELD is being produced by someEXTERNAL AGENT


17/21

ExampleA 36-m length wire carries a current

of 22A running from right to left.Calculate the magnitude anddirection of the magnetic force

acting on the wire if it is placed in amagnetic field with a magnitude of

0.50 x10-4 T and directed up thepage.

=

=

=

B

B

B

F

xF

ILBF

90sin)1050.0)(36)(22(

sin4

0.0396 N

B = +yI = -xF =

+y

+x+z

-z, into the page


18/21

WHY does the wire move?The real question is WHY does the wire move? It is easy to

say the EXTERNAL field moved it. But how can an externalmagnetic field FORCE the wire to move in a certaindirection?

THE WIRE ITSELF MUST BE MAGNETIC!!! In other words the wire has its

own INTERNAL MAGNETIC FIELD that is attracted or repulsed by theEXTERNAL FIELD.

As it turns out, the wires OWN internal magnetic

field makes concentric circles round the wire.


19/21

A current carrying wires INTERNAL

magnetic fieldTo figure out the DIRECTION of this

INTERNAL field you use the right

hand rule. You point your thumb inthe direction of the current thenCURL your fingers. Your fingers willpoint in the direction of the magneticfield


20/21

The MAGNITUDE of the internal field

The magnetic field, B, is directly proportional

to the current, I, and inversely proportional

to the circumference.

r

IB

A

Tmxx

r

IB

rBIB

o

o

2

)1026.1(104

constanttypermeabilivacuum

alityproportionofconstant

2

2

1

internal

67

o

o

=

=

=

=


21/21

ExampleA long, straight wires carries a current of 5.00 A. At one instant, a

proton, 4 mm from the wire travels at 1500 m/s parallel to thewire and in the same direction as the current. Find themagnitude and direction of the magnetic force acting on the

proton due to the field caused by the current carrying wire.

==

==

==

))(1500)(106.1(

)004.0)(14.3(2)5)(1026.1(

2

19

6

wireB

IN

oINEXB

BxF

xB

r

IBqvBF

5A

4mm+

v

2.51 x 10- 4 T

6.02 x 10- 20 N

X X X

X X X

X X X

X X XX X X

X X X

B = +zv = +yF = -x

AP Physics B - Magnetic Fields and Forces

Documents

Transcript of AP Physics B - Magnetic Fields and Forces