General Physics II. Magnetism

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Dominic Richard
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1 General Physics II Magnetism

2 Bar magnet... two poles: N and S Like poles repel; Unlike poles attract. Bar Magnet Magnetic Field lines [B]: (defined in a similar way as electric field lines, direction and density); units are Tesla [T] N S Does this remind you of a similar case in electrostatics?

3 Magnetic Monopoles Perhaps there exist magnetic charges, just like electric charges. Such an entity would be called a magnetic monopole (having + or - magnetic charge). How can you isolate this magnetic charge? Try cutting a bar magnet in half: S N S N S N Even an individual electron has a magnetic dipole! No monopoles have ever been found

4 Source of Magnetic Fields? What is the source of magnetic fields, if not magnetic charge? Answer: electric charge in motion.current! Therefore, understanding source of field generated by bar magnet lies in understanding currents at atomic level within bulk matter. Orbits of electrons about nuclei Intrinsic spin of electrons (more important effect)

5 Ferromagnetic Materials Ferromagnetic (iron, cobalt, nickel, ) In the absence of an applied B, the dipoles tend to strongly align over small patches domains. Applying an external field, the domains align to produce a large net magnetization. No Applied Field Applied Field

6 Electromagnetism We know about the existence of magnetic fields by their effect on moving charges. The magnetic field exerts a force on the moving charge. What is the "magnetic force"? Let s start with some experimental observations about the magnetic force on a charged particle: a) magnitude: to velocity of q q Fmag v b) direction: to direction of q s velocity c) direction: to direction of B Again, B is the magnetic field vector

7 Lorentz (Magnetic) Force Thus, combining these observations gives the force F on a charge q moving with velocity v through a region of space with a magnetic field B by: F= q v B sin θ Recall that the force F on a charge q in an Electric Field E is given by: F = q E

The Right Hand Rule Considering only the force on a charge in a magnetic field, we refer to this mutually perpendicular relationship by a right hand rule: Note that the RHR is for a +q charge.

8 The Right Hand Rule Considering only the force on a charge in a magnetic field, we refer to this mutually perpendicular relationship by a right hand rule: Note that the RHR is for a +q charge. The direction of the resulting force would be opposite for a q charge so it s acceptable to use the LHR!! For illustration purposes: X = vectors that point into the page = vectors that point out of the page

9 For Example.What is the direction of the missing vector (F, B, or v) in each case? B v q B v -q F v q B F(-q)

10 Three points are arranged in a uniform magnetic field. The B field points into the screen. Magnetic Force: F = qvb A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: a) right b) left c) into the screen d) out of the screen e) zero The negative charge moves from point A toward C. The direction of the magnetic force on the particle is: a) right b) left c) into the screen d) out of the screen e) zero

11 Trajectory in a Constant B Field Suppose charge q enters B-field with velocity v as shown below. What will be the path q follows? x x x x x v x q B

12 Radius of Circular Orbit Lorentz force: F = qvb Centripetal Force: Newton's 2nd Law: F = ma R = qvb mv qb x x x x x v x B v q F F = m v R 2 R

13 The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. What is the direction of the magnetic field in chamber 1? a) Up b) Down c) Left d) Right e) Into page f) Out of page

14 What is the direction of the magnetic field in chamber 2? a) Up b) Down c) Left d) Right e) Into page f) Out of page How does the magnitude of the magnetic field in chamber 1 compare to the magnitude of the magnetic field in chamber 2?

15 B-field of Straight Wire Side View End View I x I μ I B = 0 2 πr Ampere's Law µ 0 = 4π 10 7 Tm A Permeability of Free Space

16 This too obeys a right hand rule Direction of current Direction of B X X X X X Thumb along I fingers curl in direction of B

17 Think of it like a bent current-carrying wire... B-field of a Circular Loop B on the inside of the loop is out of the page R I The direction of B is the same everywhere inside the loop, so the magnetic field vectors add to give a large field near the center of the loop. µ o B = I 2R Only at the Center!

18 This too obeys a right hand rule Fingers curl in the direction of I thumb points in the direction of B

19 B-field of a Solenoid Solenoid is a number of coils packed tightly together. µ B on I L = Only near the Center! Same RHR as the single loop!!

20 Permeability As we noted earlier, some materials can be influenced be an external magnetic field to take on the characteristics of a magnet (Ferromagnetic materials). If, for example, we place one of these materials in a solenoid, the total magnetic field will be: B = B external + B material Thus, if this is the case, we replace µ 0 with a new µ called the permeability of the material. µ = K m µ 0 Where, K m is the magnetic permeability of the material; which is a constant for different substances

21 Magnetic Force on a Current-Carrying Wire Consider a current-carrying wire in the presence of a magnetic field B. There will be a force on each of the charges moving in the wire. For a straight length of wire L carrying a current I, the force on it is: F = I L B The wire obeys the same RHR as the +q charge...just replace +qv (the velocity direction of the charge) with IL (the current direction along the length of the wire) So...what is the direction of F on the wire (before and after the switch is closed) in the illustration above?

22 We now know that a current-carrying wire can experience force from a B-field. We know that a current-carrying wire produces a B-field. Therefore: We expect one current-carrying wire to exert a force on another current-carrying wire: I a I b Currents go in same direction, the wires will Currents go in opposite directions, the wires will

23 End of Magnetism Lecture

Gravity Electromagnetism Weak Strong

Gravity Electromagnetism Weak Strong 19. Magnetism 19.1. Magnets 19.1.1. Considering the typical bar magnet we can investigate the notion of poles and how they apply to magnets. 19.1.1.1. Every magnet has two distinct poles. 19.1.1.1.1. N