Gravity Electromagnetism Weak Strong

Transcription

1 19. Magnetism Magnets Considering the typical bar magnet we can investigate the notion of poles and how they apply to magnets Every magnet has two distinct poles N (north) S (south) Similar poles will repel each other Different poles will attract each other Soft magnetic material, iron, may be easily made into a magnet but it can easily lose the magnetic properties Hard magnetic material, cobalt and nickel, are difficult to magnetize but retain their magnetism Every magnet has two poles and you cannot separate them This creates the magnetic Field around the given magnet. The B-Field will always point from North to South Earth s Magnetic Field Due to the nature of the Earth s core, there is a natural magnetic field applied across the Earth. Roughly eleven degrees off of the geographic poles, the Earth s magnetic field moves from the Southern Hemisphere to the Northern Hemisphere The polarity of the magnetic field switches every few million years Magnetic Fields There are four general field forces Gravity Electromagnetism Weak Strong Weakest Strongest Largest Smallest When a charged particle moves through a magnetic field, a magnetic force acts upon it. F = qvbsin" We measure the magnetic field in Teslas B " T = N C m s F qv sin# = N Am Gauss (G) can also be used for magnetic fields where 1T =10 4 G The Earth has a magnetic field of 0.5x10 "4 T or 0.5G When the magnetic field is perpendicular to the path of the charge, the force is at a maximum value. = qvb

2 What is the force on an electron moving 30 m s perpendicular to a 3.8T magnetic field? q = "1.6x10 "19 C v = 30 m s B = 3.8T F =? F = qvb F = ("1.6x10 "19 C)(30 m s )(3.8T) F =1.82x10 "17 N To find the direction, we use the right hand rule Assume that the charge is positive Your fingers point in the direction of the moving charge Your fingers curl in the direction of the magnetic field Your thumb is now pointing in the direction of the force If the charge is negative, then the force is in the opposite direction. DO NOT USE THE LEFT HAND! Magnetic Force on a Current-Carrying Conductor A current moving through a wire is just a collection of charges moving in the same direction in some amount of time. = qvb recall that I = q "t and v = l "t = IlB Where l is the length of the wire in the magnetic field and the current and magnetic field are perpendicular A 4cm segment of a closed circuit is exposed to a B-field of 4 Tesla. What is the force in the wire is there is a independent 3.2 ohm resistor and a 12 volt power supply? V =12V F =? V = IR R = 3.2" l = 0.04m B = 4T I =? F = BIl I = 12V 3.2" = 3.75A F = (4T)(3.75A)(0.04m) F = 0.6N When drawing magnetic fields it is convention to use an X to suggest into a plane and a dot to suggest out of a plane Torque on a Current Loop and Electric Motors Now consider a loop of wire exposed to a magnetic field. The top and bottom portions feel no force B but the left is pushed out and the right is pushed in. This causes the loop to feel some torque.

3 " = BIA " = BIAsin# For a loop that is more of a collection of wound loops forming a coil and N was the number of coils we can find the torque as " = BIAN sin# For a set coil with constant current, we have the magnetic moment, µ, of the coil. " = µbsin# A circular coil, radius 80cm, is wound 18 times and placed in a 3.9T magnetic field with a current of 4.3A running through it. What is the torque on the coil? r = 0.8m " =? " = µb N =18 " = BIAN B = 3.9T I = 4.3A " = BI#r 2 N " = (3.9T)(4.3A)#(0.8m) 2 (18) " = Nm Electric Motors Function by a coil turning about in the midst of a magnetic field. As the coil rotates, the amount of magnetic field that goes through the coil changes. This is how we get alternating current and direct current Motion of a Charged Particle in a Magnetic Field When a charged particle moves through a constant magnetic field that charge will feel a constant force perpendicular to both the magnetic field and the direction of the charge. (Right Hand Rule) Because F = qvb and F"v we can relate it to any other Force that is perpendicular to the velocity. Centripetal Force. F c = m v 2 r = qvb m v 2 r = qvb r = mv qb The charge will move in a circular path with the magnetic force being directed toward the center of curvature An electron is fired into a 13T B-field at a velocity of 13.0 m s will have what radius of curvature? B =13T r =? r = mv v =13.0 m qb s q = "1.6x10 "19 C r = 5.7x10 "12 m m = 9.11x10 "31 kg

4 19.8. Magnetic Field of a Long, Straight Wire and Ampere s Law We know that a B-field exerts a force on a moving charge, but we also know a current carrying wire has a B-field Right Hand Rule # Thumb is direction of the current Fingers curl in the direction of the B-field x x x x x x x x B = µ I 0 µ 2"r 0 =permeability of free space Ampere s Law Any closed path around a curreny carrying wire has a B-field found as B "l = µ 0 I # In most cases, B = µ 0I 2"r Magnetic Force Between Two Parallel Conductors As current moves through two conductors, they magnetic field from each can will place a magnetic force on the other Consider two parallel wires separated by some distance, a, with current in the same direction F 1 = B 2 I 1 l 1 B 2 = µ 0I F 2 = B 1 I 2 l 2 B 2 = µ 0I F 1 = µ 0I 2 I 1l F 1 = µ I I l 1 *Current running in the same direction will cause an attractive force. *Current running in opposite directions will cause a repulsive force Magnetic Fields of Current Loops and Solenoids A solenoid is a tightly wound coil that has a B-field when current is run through it Staring with a single loop B = µ 0I is the B-field at the center of the loop 2R for every loop we add N to the B-field B = N µ 0I 2R

5 As the number of coils increase and the space between them decreases a solenoid is formed with a ratio between the number of coils and the length ( n = N l ). B = µ 0 ni Magnetic Domains Electrons spin while they orbit the nucleus This spin has a magnetic moment, µ Quantum Mechanics The spinning election has a unique B-field which all, typically, cancel out Ferromagnets, have domains that are lines up thus creating a constant magnetic field.