Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Lecture 13

Chapter 32

MagnetismCourse website:

http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html

03.10.2015Physics II

While performing his electric demonstration, Oersted noted to his surprise that every time the electric current was switched on, the compass needle moved.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Sources of Magnetic FieldWe have learned that electric charge q produces an electric field E

q

EIt turns out that there is another field, magnetic field B,

which is produced by moving electric charge q.

q v

moving qB

BCurrent

B Current(many q) BMagnet B(circling electrons)

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Permanent Magnet

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Permanent MagnetIn old days, people used small pieces of rocks/magnets to find the direction to the North (first compass)

If we position a compass needle in the Earth field, one side will point to the geogr. North pole.

The end of a magnet that points north is called the north-seeking pole, or simply the north pole (by CONVENTION).

The end of a magnet that points south is called the south pole.

So, note that the Earth’s “Geogr. North Pole” is really a south magnetic pole, as the north ends of magnets are attracted to it.

(Due to currents in the molten iron core)

The poles are slightly offset from the geographical poles.

In 16th century, it was discovered that the Earth is a huge magnet.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

There is no magnetic monopolesIf you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Magnets interact (repel/attract)

If the north pole of one magnet is brought near the north pole of another magnet, they repel each other.

The north pole of one magnet exerts an attractive force on the south pole of another magnet.

Like poles repel

unlike poles attract.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Notation for Vectors and Currents Perpendicular to the Page

Magnetism requires a three-dimensional perspective, but two-dimensional figures are easier to draw.

We will use the following notation:

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Magnetic Field Lines

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Magnetic Fields LinesMagnetic fields can be visualized using magnetic field lines, which are always closed loops.How to find these magnetic lines? compass needle

It is like a “probe charge”

BB

tangent to magn. field lines

magn. field stronger

magn. field weaker

The North Pole of a compass needle shows the direction of the magnetic field

https://www.youtube.com/watch?v=8llkHQtaOlg

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Oersted ExperimentIn 1819 Hans Christian Oersted discovered that an electric current in a wire causes a compass to turn.

This observation showed that there is connection between electricity and magnetism.

This is probably one of the most important experiments ever done.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Electric Current Causes a Magnetic Field

Because compass needles align with the magnetic field, the magnetic field at each point must be tangent to a circle around the wire.

The figure shows the magnetic field by drawing field vectors.

Notice that the field is weaker (shorter vectors) at greater distances from the wire.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Electric Current Causes a Magnetic Field

A tangent to a field line is in the direction of the magnetic field.

The field lines are closer together where the magnetic field strength is larger.

Magnetic field lines are imaginary lines drawn through a region of space so that:

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Electric Currents Produce Magnetic Fields

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Bio-Savart LawThe electric field produced

by a point charge

By analogy, we should have something similar for a magnetic field, B.

?

Magnetic fields, like electric fields, have been found experimentally.So, there is no derivation

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Bio-Savart LawThe magnetic field of a charged particle q moving with velocity v is given by the Biot-Savart law:

Note that the component of B parallel to the line of motion is zero.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

The Magnetic Field

The SI unit of magnetic field strength is the tesla, abbreviated as T:

1 tesla = 1 T = 1 N/A m

The constant 0 in the Biot-Savart law is called the permeability constant:

0 = 4× 10-7 T m/A = 1.257 × 10-6 T m/A

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

The Cross Product

(ab sin θ, direction given by the right-hand rule)

From now on, almost all equations will have a cross product

ConcepTest 1 B field of qA) Into the screenB) Out of the screen C) UpD) Down E) Left

What is the direction of the magnetic field at the position of the dot?

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Magnetic force on a moving charge

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

The Magnetic Force on a Moving ChargeAfter Oersted’s discovery, there were many other experiments with magnetic fields, currents, charges, etc. It was found that B exerts a force on a moving charge.

The magnetic force on a charge q as it moves through a magnetic field B with velocity v is:

where is the angle between v and B.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

The Magnetic Force on a Moving Charge

ConcepTest 2 B field of qA) To the rightB) To the left C) Into the screenD) Out of the screenE) The magnetic force is zero

The direction of the magnetic force on the proton is

ConcepTest 3 B field of qA) UpwardB) DownwardC) Into the screenD) Out of the screenE) The magnetic force is zero

The direction of the magnetic force on the proton is

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Magnetic field of a current

It is useful to rewrite the Biot-Savart law in terms of current.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

The Magnetic Field of a CurrentConsider a current I. Take a small segment ds.

Its contribution to a magnetic field at a point of observation is

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

The Magnetic Field of a Current

If we integrate this equation for an infinitely long straight wire with current, we will get:

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

What you should readChapter 32 (Knight)

Sections 32.1 32.2 32.3 32.7 32.5 (skip)

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 13

Thank youSee you on Friday