Forces Between Parallel Wires

Ampere is defined as a current at which two very long parallel wires 1 m apart create a force on each other of 2.10-7 N per meter length.

From this also follows that 0/(4) = 10-7 T.m/A

Forces Between Parallel Wires

Definition of 1 Ampere:

For long wire:

Magnetic force on lower wire: Magnetic force on upper wire:

What if current runs in opposite directions?

Forces Between Parallel Wires

Electric forces: “likes repel, unlikes attract”Magnetic forces: “likes attract, unlikes repel”

Magnetic force acts only on moving charges

Mobile electrons experience magnetic force

The motion of the wire is an electric side-effect of the magnetic force on the moving electrons.

Why does the Wire Move?

Atomic cores are not moving – no magnetic force!Atomic cores feel an unbalanced force. Wire movesdown!

X

Y

Z

Clicker Question

Metal bar

Fm

polarization

Static equilibrium:

Metal is in static equilibrium: but E 0 inside!

What is V ?

Currents Due to Magnetic Forces

Metal bar

Fm

Static equilibrium:

How much force do weneed to apply to keepthe bar moving at constantspeed?

Does this polarized bar remind you anything we’ve already studied?

Currents Due to Magnetic Forces

Fm

Non-Coulomb forcedrives e against FE

Non-Coulomb work:

What is emf of this ‘battery’?

Non-Coulomb work per unit charge:

Bar may have some resistance rint:

‘motional emf’

Non-Coulomb Work

Is round trip V zero?

EE

Round-trip Potential

Yes! Looks like any other emf.

P=IV=I(emf) Are we getting something for nothing?

Fm

Bar – current I:

FI F

Work:

Power:

Main principle of electric generators:Mechanical power is converted to electric power

Moving Bar and Energy Conservation

x

A current carrying loop has a tendency to twist in magnetic field

Compass needle: collection of atomic current loops

Magnetic Torque on a Magnetic Dipole Moment

Torque () = distance from the axle (lever arm) times perpendicular component of the force.

Works with loops of any shape!

Magnetic Torque: Quantitative Analysis

Calculate amount of work needed to rotate from angle I to f:

Potential energy for a magnetic dipole moment

Magnetic Dipole Moment: Potential Energy

Potential energy for a magnetic dipole moment

U= min-µB

0 maxµB

0

What is the energy difference between the highest and the lowest state?

Picture of the U and µ in magnetic field – important in atomic and nuclear physics.

Magnetic Dipole Moment: Potential Energy

charged tape

Any magnetic field?

Reference Frame

Two protons

+e

+e

r

1

2

v

v

Electric force:

E1

F21,e

Magnetic field:

B1 Magnetic force:

F21,m

Magnetic Forces in Moving Reference Frames

Electric force:

Magnetic force:

+e

+e

r

1

2

v

vE1

F21,e

B1

F21,m

Ratio:

(m/s)2

=c2

it is not accidental!

Magnetic Forces in Moving Reference Frames

+e

+e

r

1

2

v

vE1

F21,e

B1

F21,mFor v<<c the magnetic force is muchsmaller than electric force

How can we detect the magnetic force ona current carrying wire?

Full Lorentz force:

Magnetic Forces in Moving Reference Frames

downward

+e

+e

r

1

2

v

vE1

F21,e

B1

F21,mWho will see protons hitfloor and ceiling first?

20 ns

15 ns

Time must run slower in moving frame.

Einstein 1905: “On the electrodynamics of moving bodies”

Magnetic Forces in Moving Reference Frames

There may be different mechanisms for different observers in different reference frames, but all observers can correctly predict what will happen in their own frames, using the same relativistically correct physical laws.

The Principle of Relativity