Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Lecture 14
Chapter 33
Electromagnetic Induction
Course website:
http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII
Lecture Capture:
http://echo360.uml.edu/danylov201415/physics2spring.html
07.27.2015 Physics II
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Some stuff left uncovered from
Ch.32
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Cyclotron radius
B
The radius of the cyclotron orbit:
The period of the cyclotron motion:
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
The Cyclotron
The first practical particle accelerator, invented in the 1930s, was the cyclotron.
Cyclotrons remain important for many applications of
nuclear physics, such as the
creation of radioisotopes for
medicine.
The relevant equation for us is: . According to this equation, the
bigger the charge, the smaller the radius.
ConcepTest 1 Mass Spectrometer
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 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 x x
A B
Two particles of the same mass enter a magnetic field with the same speed and follow the paths shown. Which particle has the bigger charge?
C) both charges are equal
D) impossible to tell from the picture
Follow-up: What is the sign of the charges in the picture?
If q > 0, then the force is to the left (our case)
, ,
,
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Cloud/Bubble chamber to detect charged particles
(contains a supersaturated vapor of water)
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Magnetic on
Current-Carrying
Wires
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Magnetic Forces on Current-Carrying Wires
We saw that a magnetic field exerts a force on a charge. A current consists of many moving charges, so a magnetic field should exert a force on a current.
The magnetic force on a segment dl:
The magnetic force of a charge:
If we apply this formula for a straight wire with a current I, then we will get:
Where l is a part of wire exposed to the magnetic field
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
There’s no force on a current- carrying wire parallel to a
magnetic field.
Slide 32-139
Magnetic Forces on Current-Carrying Wires
∥
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
A current perpendicular to the field experiences a force in the direction of the right-hand rule.
Slide 32-140
Magnetic Forces on Current-Carrying Wires
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Magnetic Forces Between Parallel Current- Carrying Wires: Current in Same Direction
We’ll treat I2 as a source of the magnetic field
Let’s find a force on current I1
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Slide 32-147
Magnetic Forces Between Parallel Current-
Carrying Wires: Current in Opposite Directions
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Summary
Electric Field Magnetic Field
Amperian loop
The magnetic force on a charge:
The magnetic force on a current:
From Coulomb’s law 1
4
̂ Bio-Savart law
4
̂
Gauss’s Law
∙ ∙
The electric force on a charge:
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Electromagnetic
Induction
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Electromagnetic induction
We saw that a magnetic field could be produced with an electric current.
The question arose as to whether electric current could be produced from a magnetic field.
El. current Magn. field
El. current Magn. field
This discovery changed the world.
It allowed making electricity to power industries.
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Electromagnetic induction
By experimenting Faraday concluded that a changing magnetic field can produce an electric current, which is called an induced current.
The process is called
electromagnetic induction.
I
I
When a bar magnet is pushed into a coil of wire, it causes a momentary deflection of the current‐meter needle.
Holding the magnet inside the coil has no effect.
A quick withdrawal of the magnet deflects the needle in the other direction.
A changing magnetic field induces an EMF
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Motional EMF
Consider a conductor of length l that moves with velocity v through a perpendicular magnetic field B.
B
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Motional EMF
Let’s calculate the potential difference between ends:
∙ ∙
It is called the motional EMF
(downward, -y direction)
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
Example:
A plane flies in the Earth’s magnetic field (B = 5x10-5T) with v=1000 km/h; l=70m (between the wings)
(not very significant to consider)
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
What you should read
Chapter 32, 33 (Knight)
Sections
32.8
32.9, 10(skip)
33.1
33.2 (but skip Eddy Currents)
Department of Physics and Applied Physics
95.144, Summer 2015, Lecture 15
