L15 Ch29 Magnetism Ampere Law Combine -...

Department of Physics and Applied PhysicsPHYS.1440 Lecture 15 Danylov

Lecture 15

Chapter 29

Magnetism

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

Physics II

Bye, bye, Electricity.You won’t be missed.


Today we are going to discuss:

Chapter 29:

Section 29.1-3 Section 29.5 (skip) Section 29.7


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

qE

It turns out that there is another field, magnetic field B,which is produced by a moving electric charge q.

q v

(I) Moving qB B

Current

B (II) Current(many q) B (III) Magnet B(orbiting electrons)

B

So, there are three systems producing B field. Let’s look at them separately.


(III) Permanent Magnet


Magnets interact (repel/attract)

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

Like poles repel Unlike poles attract.

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


There are 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.

Sheldon: “if I’m able to detect slow‐moving magnetic monopolesthere, I will be the scientist to confirm string theory. People willwrite books about me. Third‐graders will create macaroni‐artdioramas depicting scenes from my life.”

His friends tampered with his experiment on magnetic monopoles by using an electric can opener.

There is no magnetic monopole

One of the “Big Bang Theory” episodes was arranged around this fact.

There is no experimental evidence that magnetic monopoles exist.

A number of attempts have been made to detect magnetic monopoles.

Sheldon Cooper has also made one:


Probe object. Magnet Pole Convention

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

(I) The end of a needle that points to the North geograph. pole is called the north pole (by CONVENTION).The end of a magnet that points south is called the south pole.As the result, if we follow the convention, the Earth’s “Geogr. North Pole” is a south magnetic pole, as the north end of the compass needle is attracted to it.The magnetic poles are slightly offset from the geographical poles.

*The Earth is a huge magnet due to currents in the molten iron core.

North Magnetic Pole

South Magnetic Pole

Again?

Now, we know that the magnetic field (B) exists. How can we detect B? Which object can be used as a probe system?

(0) A compass needle will be used as a probe system.

Which side of the needle should be called the North pole?Lets use the Earth’s Magnetic field*

(II) The North pole of a compass shows the direction of the magnetic field at the point.


Magnetic Fields Lines

Magnetic fields can be visualized using magnetic field lines, which are always closed loops (consequence of the fact that there are no magnetic monopoles).

How to find these magnetic lines? With a compass needlelike a “probe charge”

B

Density of magn. lines is smaller so the magn. field is weaker

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

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

(II) Density of magn. lines is higher so the magnetic field is stronger

Demo:Iron filings are suspended in liquid in a clear rectangle box.

Now, since we have a probe system, a compass needle, we can use it to map a magnetic field of, for example, a permanent magnet.


Vector notation and the cross (vector) product

Before we proceed with magnetic field we need to look at


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:

Bad karma


The Cross Product

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

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

The cross product of vectors a and b is a vector perpendicular to both a and b.

[I] Point fingers in the direction of the 1st (a) vector, then bend them in the direction of the 2nd one (b).The outstretched thumb will give a direction of the cross product

[II] Use three fingers as shown in the figure

Order is important in the cross product:

ConcepTest Cross Product

Find a direction of a cross product


(I) Bio-Savart Law

The 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

describes magnetic field of a moving charge


Bio-Savart LawThe magnetic field of a charged particle q moving with velocity v is given by (I) the Biot-Savart law (for a point charge):

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

(II) Biot-Savart law (for a current)Consider a current I. Take a small segment ds.Its contribution to a magnetic field at a point of observation is:

q Iv ds


The Units of B

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

200‐ton superconducting magnet (Argonne National Laboratory)

ConcepTest 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?


Magnetic field of an infinitely long straight wire with current

If we integrate the BS law equation

2d a perpendicular distance from the wire.

Use a Compass!(RHR#2)

(This integration is not trivial, so we skip it and derive the formula later using Ampere’s Law)B‐?

How can we find a B direction?And you’ll get this:

For the sake of our conveniences RHR#2 was introduced.

for an infinitely long straight wire with current, we will get:

ConcepTest B field of two wiresA) upB) downC) rightD) left E) Into the page

What is the direction of the magnetic field at the position of the dot equidistant to both currents?

fieldWire 1 with current I

Wire 2 with current I


Oersted ExperimentIn 1819 Hans 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.

It was a demonstration that an electric current produces magnetic field.

While performing his electric demonstration, Oersted noted to his surprise that every time the electric current was switched on, the compass needle moved.https://www.youtube.com/watch?v=Gtp51eZkwoI

(History of Electricity, start at 1.04.20)


Thank you

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