PHYSICS 51: Ch. 27 lectures

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PHYSICS 51: Ch. 27 lectures. Homework #8: Magnetic Fields. Read Ch. 27.1 - 27.7 We will talk a bit in class about sections 8 and 9 also Do Exercises : Ch 27, #1, # 16, # 42, #46, #74 Due: Thursday April 3. 2014. First Section Electric Forces Electric Fields Electric Potential

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### PHYSICS 51: Ch. 27 lectures

Homework #8: Magnetic Fields
• Read Ch. 27.1 - 27.7
• We will talk a bit in class about sections 8 and 9 also
• Do Exercises :Ch 27, #1, #16, #42, #46, #74
• Due: Thursday April 3. 2014
First Section

Electric Forces

Electric Fields

Electric Potential

Second Section

Resistance

Capacitance

DC Circuits

Third Section

Magnetic Forces

Magnetic Fields

Induction

Fourth Section

AC Circuits

Electromagnetic Fields (Waves)

Physics 51
Magnetic Fields
• Big difference between Electric and Magnetic fields is that there in no magnetic monopole
• No simple source of the field (see Maxwell’s Equations)
• Magnetic field created by moving charge!
• Field interacts with another moving charge
• Text Ch 27: How charge reacts to Magnetic field
• Text Ch 28: How to create Magnetic field

MAXWELL’S EQUATIONS

The relationships between electric and magnetic fields and their sources can be stated compactly in four equations, called Maxwell’s equations. Together they form a complete basis for the relation of E and B fields to their sources.

C 2004 Pearson Educational / Addison Wesley

Earth’s Magnetic Field
• Earth’s magnetic field caused by convection currents in the molten core (we think)
• Compass
• Invented 2,000 years ago in China, used more for Fung Shui than navigation
• Critical to the age of sail and exploration
• Magnetic north pole and rotational north pole far apart
• Magnetic north pole moves around
• Field flips every few thousand years
• Provides protection from cosmic rays
• Connection between magnetic field and electric currents first observed about 1820 until then thought of as separate subjects
Earth’s Magnetic Field
• Earth’s magnetic field caused by convection currents in the molten core (we think)
• Compass
• Invented 2,000 years ago in China, used more for Fung Shui than navigation
• Critical to the age of sail and exploration
• Magnetic north pole and rotational north pole far apart
• Magnetic north pole moves around
• Field flips every few thousand years
• Provides protection from cosmic rays
• Connection between magnetic field and electric currents first observed about 1820 until then thought of as separate subjects
Example: Force Calculation

An proton, with a speed of 1 x 106 m/s enters a region where the magnetic field is into the paper. The field strength is .1 T. What is the pattern of the flight of the proton. What is the rdius of curvature?

mp= 1.6 x 10-28 Kg, e = 1.6 x 10-19 C

Particle in Constant Magnetic Field

Orbit of a charged particle in a uniform magnetic field is a circle

R = m v / q B

Example #2
• An electron comes out of the board at the front of the room. Assume the local magnetic field is up toward the sky. Which direction is the electron bent?
Plan for the day
• Moving Charge in Magnetic Field
• Mass Spectroscopy
• Force on a current in a wire
• Audio Speaker
• Torque on a loop in a Magnetic Field
• DC Electric Motor
• Quiz
Fields and forces: Review

Electric Field

• Charge creates field (E)
• Field interacts with different charge causing force

Magnetic Field

• Moving charge creates field (B) (Ch 28)
• Vector field like E
• Field interacts with moving charge causing force
• Unit of B is T (Tesla) = N/Am
• 104 Gauss = 1 T

Magnetic force acting on a moving (+) charge

Force is perpendicular to both velocity and field

q v B = q E

v = E / B

Velocity selector for charged particles uses perpendicular E and B fields, only one velocity goes straight

I

Force on a moving positive charge in a current-carrying conductor:

L

F = I L x B

For vector direction use “RIGHT HAND RULE”

I

Right hand rule

F = I L x B

Magnetic force on a straight wire carrying current Iin a magnetic field B

Example

A 10.0 cm segment of wire carries a 5.0A current as shown. It is in a uniform 2.0T magnetic field. What is the magnitude and direction of the force on the wire? What orientation gives a maximum force?

B field

Wire, 45 degrees to field

A rail gun!

F = I L x B

Dynamic Loudspeaker Principle

A current-carrying wire in a magnetic field experiences a magnetic force perpendicular to the wire.

Loop of current

A square loop of wire, 10.0 cm on a side sits in the xy plane. It carries a current I0.0 mA through the loop going clockwise when viewed from above. The loop sits in a constant magnetic field of 0.5T in the +x direction.

• What is the magnitude of the net force on the loop
• What is the magnitude of the net torque on the loop

Forces on the sides of a current-carrying loop in a uniform magnetic field.This is how a motor works!

Magnetic Moment
• Electric Dipole Moment
• Definition: p = qd
• Torque:  = p x E
• Magnetic Dipole Moment
• Definition  = niA
• Torque  =  x B

Magnetic Moment

Right hand rule determines the direction of the magnetic moment () of a current-carrying loop

Torque (m x B) on this solenoid in a uniform magnetic field is into the screen thus rotating the solenoid clockwise

Magnetic Moment

Right hand rule determines the direction of the magnetic moment () of a current-carrying loop

Torque (m x B) on this solenoid in a uniform magnetic field is into the screen thus rotating the solenoid clockwise

Atomic Magnetic Moments
• Electrons and Protons also have magnetic moments (spin)
• Zeemann effect is the splitting of and atomic transition based on the energy associated with the electron spin in an magnetic field
• Atoms have magnetic moments associated with electron “orbiting” the nucleus
• Ferromagnetic Materials have “domains” of aligned magnetic moments
• You can expand domains with applied magnetic field
• Iron can be made into a permanent magnet

Magnets are aligned magnetic moments

Atomic magnetic moments in an iron bar (a) unmagnetized

(b) magnetized (c)Torque on a bar magnet in a B field

If the Field is non-uniform you can cause a net force

Current loops in a non-uniform B field