Magnet Forces and Magnetic Fields

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1 Magnet Forces and Magnetic Fields

description

Magnet Forces and Magnetic Fields. 1) Magnets and Magnetic Fields. a) Natural permanent magnets Like poles repel, unlike attract come in pairs (no monopoles) Interact with earth; define N (or north-seeking) pole as pole attracted to North pole of earth. b) Magnetic field direction: - PowerPoint PPT Presentation

Transcript of Magnet Forces and Magnetic Fields

Page 1: Magnet Forces and Magnetic Fields

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Magnet Forces and Magnetic Fields

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1) Magnets and Magnetic Fields

a) Natural permanent magnets– Like poles repel, unlike attract– come in pairs (no monopoles)– Interact with earth;

define N (or north-seeking) pole as pole attracted to North pole of earth

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b) Magnetic field direction:

- direction of force on N pole

B

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c) Field of dipole

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d) Magnetostatics for poles

(identical to electrostatics for charges)– 2 types: N, S vs +,-– Unlike attract, like repel– Inverse square law– Force along joining line– Magnetic Field:

B

F

qM

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e) Why study magnetism?– No monopoles (yet)– Poles (dipoles) produced by moving charges (no direct

control of pole distribution)– Charges affected by magnetic field

i.e. fundamental unit is still charge; want magnetic field due to charge, and force on charge due to magnetic field

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2) Magnetic field due to current (direction)

• Oersted (1820)

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B I

r

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3) Magnetic force on current

Direction from RHR1: B fingers, I thumb, F palm

F

IB

Force per unit length

defines B

a) Orthogonal case

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Bearth .5 gauss 5 10 5 T

Bfridge magnet .01T

Bsuper conducing 1 10 T

B F

I

N

Amtesla (T)Units:

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b) General case

F

LIBsin

Force per unit length

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4) Force between parallel wires

B I1

d;

F

I2B

F

k

I1I2

d

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Attraction or repulsion?

Does it depend on reference frame?

+

+

FE

FE

FB

FB

v

v

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v

v

+

+

-

-

+

+

-

-

+

+

-

-

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• Define Ampere as the quantity of current that produces a force per unit length of 2 x 10-7 N/m for separation of 1 m

F

k

I1I2

d

k 1

40

8.988 109Nm2/C2

k (2 10 7 N/m)(1m)

(1A2)2 10 7N/A2• Then

• This defines C and gives

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• Permeability of free space

0 2 k

F

0

2I1I2

dThen

4 10 7N/A2

k 0

2

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5) Field due to long straight wire (magnitude)

B I

r

B 0

2I

r

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6) Force on a moving charge

• Zero at rest

• Zero parallel to B

• Max perpendicular to B

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F qvBsin(Alternative definition of B)

• Proportional to component of v perp to B

• Perpendicular to B

• Perpendicular to v

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7) Motion of a charge in a magnetic field

a) Constant force

motion is parabolic

electric or gravitational field

not everywhere perp to velocity

not magnetic field

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b) Constant magnitude perpendicular to motion

radial field (circular motion)

mass on a string

magnetic field produces circular motion

(initial vel. perp. to B)

motion is circular

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F Fc mv 2

r

Force due to the field:

F qvB

For circular motion:

So,

mv 2

rqvB

r mv

qBr depends on v, B

v

r

qB

m

angular freq. independent of speed, radius

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Tracks in a bubble chamber

• electron-positron creation

• 1, 3 positive

• 2 negative

• energy: 3 > 2 > 1

• energy decreases by collisions

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Example: Find speed and radius for proton

B = 0.10 T

V = 2100 V

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c) Work done by magnetic field

W Fx cosF

displacement, x

Work by a force F

For a magnetic field,

0

Work = 0

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d) Velocity selector

FE qE

Force due to E (down):

Force due to B (up):

FB qvB

For zero deflection, FE = FB :

qE qvB

v E

B

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e) Mass SpectrometerIon energy:

KE 12 mv 2 qV

v 2qV

m

Radius of motion:

r mv

qB

m

qB

2qV

m

r m

q

2V

B

m

q

r2B2

2V