Department of Physics and Applied Physics95.144 Danylov Lecture 14

Lecture 14

Chapter 32

Magnetism

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

Physics II

Department of Physics and Applied Physics95.144 Danylov Lecture 14

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.

Department of Physics and Applied Physics95.144 Danylov Lecture 14

(III) Permanent Magnet

Department of Physics and Applied Physics95.144 Danylov Lecture 14

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.

Department of Physics and Applied Physics95.144 Danylov Lecture 14

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:

Department of Physics and Applied Physics95.144 Danylov Lecture 14

Magnet Pole ConventionIn old days, people used small pieces ofrocks/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 geographical North pole.

The end of a magnet that points north is called the north pole (by CONVENTION).The end of a magnet that points south is called the south pole.

As the result, 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 magnetic poles are slightly offset from the geographical poles.

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

North Magnetic Pole

South Magnetic Pole

Again?

Department of Physics and Applied Physics95.144 Danylov Lecture 14

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”

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

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

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

ConcepTest 1 Compass/Magnet

A) ClockwiseB) CounterclockwiseC) No rotation

The compass needle is free to rotate in the plane of the page. In which direction does the needle rotate?

NS

Pivot

Department of Physics and Applied Physics95.144 Danylov Lecture 14

Vector notation and the cross (vector) product

Before we proceed with magnetic field we need to look at

Department of Physics and Applied Physics95.144 Danylov Lecture 14

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 Danylov Lecture 14

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 1 Cross Product

Find a direction of a cross product

Department of Physics and Applied Physics95.144 Danylov Lecture 14

(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

Department of Physics and Applied Physics95.144 Danylov Lecture 14

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 Danylov Lecture 14

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

200‐ton superconducting magnet (Argonne National Laboratory)

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 Danylov Lecture 14

(II) Magnetic field of a current

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

End

Department of Physics and Applied Physics95.144 Danylov Lecture 14

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.

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

https://www.youtube.com/watch?v=‐w‐1‐4Xnjuw

(Start at 1.00 min)

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)

Department of Physics and Applied Physics95.144 Danylov Lecture 14

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 Danylov Lecture 14

Magnetic field of an infinitely long straight wire with current

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

Magnitude of B at a perpendicular distance d from the wire.

How to find a direction of B? Use a Compass!

For the sake of convenience,the right-hand rule was introduce

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

B

Notice that the field is weaker at greater distances from the wire.

B‐?

ConcepTest 1 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

Department of Physics and Applied Physics95.144 Danylov Lecture 14

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 Danylov Lecture 14

Thank youSee you on Friday