Magnets We have all seen the demonstration where you put a magnet under a piece of glass, put some iron filings on top and see the effect. What you are seeing is another invisible force field known as a magnetic field. 1
Magnets A force is applied to the iron filings causing them to align themselves to the direction of the magnetic field. A compass needle will tell you the direction of the field. Show Fields of little compasses Magnetic vs. Electric This is similar to another field we have talked about an electric field. Magnetic Field Electric Field 2
Magnetic vs. Electric An electric field came about from the attraction of [+] and [-] charges. Magnetic Field Electric Field Magnetic vs. Electric Magnetic Fields come about from the attraction of North and South Poles. These exist in naturally magnetic materials or can be created in temporary magnetic materials, ferromagnetic materials. Magnetic Field Electric Field 3
Magnetic vs. Electric [+] and [-] charges came about from either charged particles, or charge separation. Magnetic Field Electric Field Magnetic vs. Electric [N] and [S] poles come about from the orientation of electrons inside magnetic materials known as domains. Magnetic Field Electric Field 4
Magnetic vs. Electric E denotes the electric field strength. B denotes the strength of a magnetic field. Magnetic Field Electric Field Magnetic Fields Magnetic Fields can be drawn the same way as electric fields. We use field lines to show the direction of the field, which runs from the north pole to the south pole. The closer the lines are together, the stronger the field. The arrow on an magnetic field diagram denotes the direction the north needle of a magnetic compass would point if placed in that field, which means it points to the south pole. 5
Magnetic Fields Magnetic Fields The strength of a magnetic field also depends on the placement of multiple magnets. 6
Earth s Magnetic Field The Earth has a magnetic field. Earth s Magnetic Field Compasses point to the North Geographic Pole 7
Earth s Magnetic Field Which is actually the South Magnetic Pole. Why are things Magnetic? Objects are made of elements with electrons. Electrons have a spin orientation, known as a magnetic moment. When groups of atoms have the same magnetic moment they make up magnetic domains. In most materials domain directions are random but in some materials they are aligned, making them magnetic. 8
Domains Magnetizing Some materials (like Iron and Cobalt) allow their magnetic moments to become aligned. This is done by placing them in a magnetic field which causes their domains to align to that field. When the field is removed the domain can stay aligned for a long time. However, heat and vibration can knock them back out of alignment. 9
Magnetizing Link to animation Magnetic Fields Magnetic Fields can also affect the motion of charged objects. However, a magnetic field only applies a force on a moving particle. The force applied on a charged object due to a magnetic field depends on The strength of the field [B] The charge of the particle [q] The speed of the charged particle [v] 10
Magnetic Field Strength The strength of a magnetic field [B] is similar to the quantity [E], electric field strength. Just as E was a force per charge, B is a force per charge at some point. E did not care about the speed of the charge, but B does, so it is really a force per charge that also depends on the objects velocity at that point. And since they are all vectors, it really only cares about the part of the particle s velocity that is perpendicular to the field. The Magnetic Field Defined Putting this all together, we can define the magnetic field as its affect on a test charge moving at a velocity at some point in the field. F B F q v So the force a particle feel would be F qv B q v B sin (Vector Cross Product) (Magnitude) 11
Units of Magnetic Field The units of magnetic field are Tesla. newton coulomb meter / second 1 Tesla T Teslas are big, so Magnetic Fields are often given in terms of Gauss, where 10,000 G = 10 4 G = 1 T B F q v Direction of the Magnetic Force The direction of an electric force was along a field line away from [+] charges. The direction of magnetic forces on moving charges are a little more odd. The direction of a magnetic force is NOT in the direction of the magnetic field lines, but rather perpendicular to BOTH the field lines AND the part of the velocity of the particle that is perpendicular to the field. 12
Direction of the Magnetic Force The force is at it max when they are all perpendicular to each other. Direction of the Magnetic Force As the angle goes out of perpendicular, the size of the magnetic force decreases. 13
Direction of the Magnetic Force Until it goes to zero when the velocity is in the same direction as the field. Right Hand Rule To determine the direction of the force easier, we use the RIGHT HAND RULE. It is as follows Hold your right hand open. Place your fingers in the direction of the magnetic field (lots of lines). Your thumb goes in the direction of the velocity of the particle (like when you hitch a ride). Then the direction of a force on a positive charge will be OUT OF your palm (Bam! Slap!). 14
Right Hand Rule Force on a Wire If a magnetic field exerts a force on a single moving charge it makes sense that it would exert a force on a current carrying wire. WHY? 15
Force on a Wire A current is really many moving charges. So the force it would feel would be the sum of the forces on all these charges. Force on a Wire To find the total force, we have to multiply the force on each by the number of charges. From previous chapters, we know that F max q v B F B I I q t sin 16
Force on a Wire You can use the same Right Hand Rule to describe the direction of the force, but remember the direction of the velocity of the charges is really in the direction of the current. Fingers in direction of B field Thumb in direction of current (velocity) Palm in direction of force Ferroliquids 17
Ferroliquid Art Superconductive Levitation and Suspension 18
Diamagnetic Floating Frog STOP HERE Do a few examples (Sample prob 1, 2, 3) 19
Motion of a Particle in B When a moving particle is in a magnetic field, it feels a force that is always perpendicular to its velocity. As it turns out as the direction of v changes, the direction of F changes making it turn more. The result is that it travels in a circular path. We can equate the centripetal force to the magnetic force ( = 0). If we solve for the r, we can find the radius that the particle will curve at. Motion of particle in B F mv 2 F c r q v B sin If = 90 r mv qb The faster the particle, the wider the curve. 20
Motion of Particle in B The Force is always oriented towards the center of its circular path, the velocity is always oriented perpendicular to it. Therefore a magnetic field never changes the speed of a charged particle, only its direction. Sample Prob 4,5 (FAN) Particle Traces The fact that charged particles move in curved paths in a magnetic field is used to determine what particles remains after atomic collisions but use of particle traces. A big v would have a: A big m would have a: A big q would have a: What about period? 21
CRT Televisions This is how CRT TVs work. Energetic electrons are fired at a screen through a magnetic field. The field is controlled to bend the electrons to hit the screen at a certain spot. The screen fluoresces when an electron hits it, and creates an image. That is why you get interference when a magnet is brought near a TV screen, the electrons creating the image are getting bent, making a distorted image. E and B together Certain mechanisms use a combination of E and B fields move particles in straight lines or to select particles at certain velocities. These are called velocity selectors, or mass spectrometers. Derivation of what happens in combined field Do Sample Problem 6 from Follow Along Notes Do Sample AP Problem 22
Magnetic Field of a long wire We know a current carrying wire can feel a magnetic force when placed in a field. It also creates its own magnetic field. We can use a second Right Hand Rule to determine the direction of this field. RHR 2: Right Thumb in direction of current. Curl your fingers, and they point in the direction of the created magnetic field. Right Hand Rule 2 Right Thumb in direction of current. Curl your fingers, and they point in the direction of the current. 23
Magnitude of Field from a Wire It has been found experimentally that the magnitude of a magnetic field produced by a wire is: B 0 2 I r Combination of B The magnetic field [B] is a vector, so the total field from multiple sources can be combined as any vectors are. For example, the magnetic field produced from two long wires can be found as: B 0I1 0I2 0 I1 I 2 r1 2 r2 2 r1 r 2 2 24
Force on Two Wires Two wires that carry current placed near each other will apply a force on each other. To find the value of the force, you only have to use the previous equation, in its two forms. Let s see Mr. Maloney derive it. Force on 2 Wires F I 0 1 2 I r 2 25
Forces (Torque) on a Loop Just as a straight wire will experience a force in a magnetic field, a loop of wire will also experience a force. This force will cause it to spin, so we call it a torque. Because the current is flowing in different directions on each side, each side will see a force in the opposite direction. The loop will tend to rotate such that its normal becomes aligned with the magnetic field. At this point, the forces are directly opposite each other, and will tend to hold the loop still. Forces on a Loop 26
DC Motor (simple motor) Solenoid/Electromagnet A coil of wire can be used to create a strong magnetic field. Each coil created a magnetic field vector pointing along the center axis. This is how simple electromagnets are made. Put a ferromagnetic core inside it and make it even more powerful. Show Solenoid Animation and Examples ElectroMagnet Tube Show Magnet Gun 27