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1 Lecture 13 Chapter 29 Magnetism Course website:

2 Today we are going to discuss: Chapter 29: Section Section 29.5 (skip) Section 29.7

B) First, it is bright, then dim. C) First, it is dim, then bright. D) Steady bright.

3 ConcepTest RC circuit 1 In the circuit shown, the capacitor is originally uncharged. Describe the behavior of the lightbulb from the instant switch S is closed until a long time later. A) No light. B) First, it is bright, then dim. C) First, it is dim, then bright. D) Steady bright. When the switch is first closed, the current is high and the bulb burns brightly. As the capacitor charges, The voltage across the capacitor increases causing the current to be reduced, and the bulb dims.

4 Sources of Magnetic Field We have learned that electric charge q produces an electric field E E q It turns out that there is another field, magnetic field B, which is produced by a moving electric charge q. q B v (I) Moving q Current B 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.

5 (III) Permanent Magnet

6 Magnets interact (repel/attract) If the north pole of one magnet is brought near the north pole of another magnet, they repel each other. Like poles repel The north pole of one magnet exerts an attractive force on the south pole of another magnet. Unlike poles attract.

There are no magnetic monopoles If you cut a magnet in half, you don t get a north pole and a south pole you get two smaller magnets. One of the Big Bang Theory episodes was arranged around this fact.

7 There are no magnetic monopoles If you cut a magnet in half, you don t get a north pole and a south pole you get two smaller magnets. One of the Big Bang Theory episodes was arranged around this fact. There is no magnetic monopole 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: Sheldon: if I m able to detect slow moving magnetic monopoles there, I will be the scientist to confirm string theory. People will write books about me. Third graders will create macaroni art dioramas depicting scenes from my life. His friends tampered with his experiment on magnetic monopoles by using an electric can opener.

Magnet Pole Convention In old days, people used small pieces

compass) In 16 th century, it was discovered that the Earth

(Due to currents in the molten iron core) Again?

Earth field, one side will point to the geographical North

8 Magnet Pole Convention In old days, people used small pieces of rocks/magnets to find the direction to the North (first compass) In 16 th century, it was discovered that the Earth is a huge magnet. (Due to currents in the molten iron core) Again? South Magnetic Pole 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. The magnetic poles are slightly offset from the geographical poles. North Magnetic Pole

9 Magnetic Fields Lines Magnetic fields can be visualized using magnetic field lines, which are always closed loops. How to find these magnetic lines? Density of magn. lines is higher so the magnetic field is stronger B compass needle It is like a probe charge The North Pole of a compass needle shows the direction of the magnetic field Density of magn. lines is smaller so the magn. field is weaker Demo: Iron filings are suspended in liquid in a clear rectangle box.

10 ConcepTest Compass/Magnet The compass needle is free to rotate in the plane of the page. In which direction does the needle rotate? A) Clockwise B) Counterclockwise C) No rotation S N Pivot

11 Before we proceed with magnetic field we need to look at Vector notation and the cross (vector) product

12 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:

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

direction of the 1 st (a) vector, then bend them in the direction of the 2 nd

The outstretched thumb will give a direction of the cross product [II] Use

13 The Cross Product From now on, almost all equations will have a cross product =(ab sin θ, direction given by the right-hand rule) [I] Point fingers in the direction of the 1 st (a) vector, then bend them in the direction of the 2 nd one (b). The outstretched thumb will give a direction of the cross product [II] Use three fingers as shown in the figure The cross product of vectors a and b is a vector perpendicular to both a and b. Order is important in the cross product:

14 ConcepTest Cross Product Find a direction of a cross product

15 (I) Bio-Savart Law describes magnetic field of a moving charge 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

16 Bio-Savart Law The 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.

17 The Magnetic Field The constant 0 in the Biot-Savart law is called the permeability constant: 0 = T m/a = T m/a The SI unit of magnetic field strength is the tesla, abbreviated as T: 1 tesla = 1 T = 1 N/A m 200 ton superconducting magnet (Argonne National Laboratory)

18 ConcepTest B field of q A) Into the screen What is the direction of the magnetic field at B) Out of the screen the position of the dot? C) Up D) Down E) Left

19 End (II) Magnetic field of a current It is useful to rewrite the Biot-Savart law in terms of current.

This observation showed that there is connection between electricity and magnetism. https://www.youtube.com/watch?

20 Oersted Experiment In 1819 Hans Christian Oersted discovered that an electric current in a wire causes a compass to turn. It was a demonstration that an electric current produces magnetic field. This is probably one of the most important experiments ever done. This observation showed that there is connection between electricity and magnetism. (History of Electricity, start at ) (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. w 1 4Xnjuw

21 The Magnetic Field of a Current Consider a current I. Take a small segment ds. Its contribution to a magnetic field at a point of observation is

integrate this equation for an infinitely

get: (This integration is not trivial, so

22 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: (This integration is not trivial, so we skip it and derive the formula later using Ampere s Law) 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 B? B Notice that the field is weaker at greater distances from the wire.

23 ConcepTest What is the direction of the magnetic field at the position of the dot equidistant to both currents? B field of two wires A) up B) down C) right D) left E) Into the page field Wire 1 with current I Wire 2 with current I

24 Thank you See you next time

Elements of Physics II. Agenda for Today

Elements of Physics II. Agenda for Today Physics 132: Lecture e 18 Elements of Physics II Agenda for Today Magnets and the Magnetic Field Magnetic fields caused by charged particles B-field from a current-carrying wire Magnetic fields and forces