Slide 1

The Magnetic Field Physics Montwood High School R. Casao Slide 2 Our most familiar experience of magnetism is through permanent magnets. Inside a magnetized body, such as a permanent magnet, there is a coordinated motion of certain electrons; in an unmagnetized body, the electron motions are not coordinated. These are made of materials which exhibit a property we call ferromagnetism - i.e., they can be magnetized. An unmagnetized piece of iron can become a permanent magnet by being stroked with a permanent magnet If a piece of unmagnetized iron is placed near a strong permanent magnet, the piece of iron will eventually become magnetized. A magnetized object can lose its magnetic properties by heating and cooling the iron or by hammering the iron. Slide 3 Magnetic materials can be described as hard or soft, depending upon the extent to which they retain their magnetism. Soft magnetic materials, such as iron, are easily magnetized but also tend to lose their magnetism easily. Hard magnetic materials, like cobalt and nickel, are difficult to magnetize, but once they are magnetized, they tend to retain their magnetism. The magnetic properties of many materials are explained in terms of a model in which an electron is said to spin on its axis (remember the up and down arrows in the orbital notation you used in chemistry ). The spinning electron is a charge in motion that produces a magnetic field. Slide 4 In atoms with many electrons, the electrons usually pair up with their spins opposite each other, and their magnetic fields cancel each other. This is why most substances are not magnetic. In ferromagnetic materials such as iron, cobalt, and nickel, the magnetic fields produced by the electron spins do not cancel completely. Strong coupling occurs between neighboring atoms to form large groups of atoms whose net spins are aligned; these groups are called domains. In an unmagnetized substance, the magnetic domains are randomly oriented. In magnetized materials, whether permanent or temporary, the domains are aligned. Slide 5 unmagnetized magnetized Slide 6 In hard magnetic materials, the domain alignment remains after the external magnetic field is removed. In soft magnetic materials, once the magnetic field is removed, the random motion of the particles in the material changes the orientation of the domains back to a random arrangement. Heating and hammering can cause the domains in hard magnetic materials to become randomly arranged, resulting in a loss of the permanent magnetic properties. Depending on how we position two magnets, they will attract or repel, i.e. they exert forces on each other. Thus, a magnet must have an associated field: a magnetic field. We describe magnets as having two magnetic poles: North (N) and South (S). Magnetic poles always occur in pairs. Slide 7 When a magnet is broken in half, equal and opposite poles appear at either side of the break point. The result is two magnets, each with a north and south pole. Slide 8 A compass is used to detect the presence of a magnetic field. The needle of a compass is a piece of magnetized iron. The compass needle aligns with the magnetic field at the needles position. The north pole of a compass needle is attracted toward the geographic north pole of the Earth and repelled by the Earths geographic south pole. An object that contains iron but is not itself magnetized (shows no tendency to point north or south) is attracted by either pole of a permanent magnet. This is the attraction that acts between a magnet and the unmagnetized steel door of a refrigerator. Slide 9 Only iron and a few other materials, such as cobalt, nickel, gadolinium, and some of their oxides and alloys, show strong magnetic effects and are said to be ferromagnetic. Other materials show more slight magnetic effect. The Earth itself is a large magnet. Geophysicists generally agree that the Earths magnetic poles arise from currents in its molten iron core. The magnetic poles are offset slightly from the geographic poles of the Earths rotation axis. The geographic north pole is actually a south magnetic pole. Slide 10 Slide 11 We used the concept of an electric field surrounding an electric charge. Similarly, we can imagine a magnetic field surrounding a magnet. The force one magnet exerts on another can be described as the interaction between one magnet and the magnetic field of the other. We can also draw magnetic field lines. For magnetic field lines: The number of lines per unit area is proportional to the strength of the magnetic field. The field lines are closer together where the magnetic field is stronger. The direction of the magnetic field is tangent to a field line at any point. Slide 12 The direction of the magnetic field at a given point is defined as the direction that the north pole of a compass needle would point if placed at that point. Magnetic field lines always point out from the north pole and toward the south pole of a magnet. Magnetic field lines continue inside the magnet to form closed loops. Slide 13 Slide 14 Slide 15 The origin of magnetism lies in moving electric charges. Moving (or rotating) charges generate magnetic fields in the surrounding space in addition to its electric field. An electric current generates a magnetic field. A magnetic field will exert a force on a moving charge that is present in the field. A magnetic field will exert a force on a conductor that carries an electric current in the field. The magnetic field is a vector field associated with each point in space. The symbol for the magnetic field if B. Slide 16 We can define a magnetic field B at a point in space in terms of the magnetic force F B that the field exerts on a charged particle moving with a velocity v. Experiments on charged particles moving in a magnetic field give the following results: The magnitude F B of the magnetic force exerted on the particle is proportional to the magnitude of the charge q. If a 1 C charge and a 2 C charge move through the same magnetic field with the same velocity, experiments show that the force on the 2 C charge is twice as great as the force on the 1 C charge. The magnitude F B of the magnetic force exerted on the particle is proportional to the magnitude, or strength, of the field B. If we double the magnitude of the field without changing the charge or its velocity, the force doubles. Slide 17 The magnitude F B of the magnetic force exerted on the particle is proportional to the speed v of the particle. A charged particle at rest experiences no magnetic force. The magnetic force F B does not have the same direction as the magnetic field B but instead is always perpendicular to both B and the velocity v. The magnitude F B of the magnetic force is proportional to the component of the velocity perpendicular to the field. The maximum magnetic force F B occurs when the magnetic field B and the velocity v are at right angles to each other. The magnetic force F B is zero when the magnetic field B and the velocity v are parallel (0) or antiparallel (180). Slide 18 Slide 19 The direction of F B is always perpendicular to the plane containing B and v. Equation: q is the magnitude of the charge (drop any negative signs on charges) is the angle between the direction of v and the direction of B. Slide 20 The direction of the magnetic force F B is given by the right hand rule: Point the fingers of your right hand in the direction of the velocity vector v. Point the palm of your right hand in the direction of the magnetic field vector B. The thumb of your right hand points in the direction of the magnetic force F B. Slide 21 Casaos Version of the Right-Hand Rule I use the right hand as described for positive charges. No change here. I use the left hand for negative charges. Point the fingers of the left hand in the direction of the velocity vector v. Point the palm of the left hand in the direction of the magnetic field vector B. The thumb of the left hand points in the direction of the magnetic force F B. Slide 22 If the magnetic field B is directed into the page, crosses represent the tail of the vector arrow. If the magnetic field B is directed out of the page, dots represent the head of the vector arrow. The units of the magnetic field B is the Tesla and the abbreviation is T. An older unit for the magnetic field is the Gauss (1 G = 0.0001 T). Slide 23 Magnetic Force on a Current-Carrying Conductor A magnetic force is exerted on a single charged particle when the particle moves through a magnetic field, so a current-carrying wire placed in a magnetic field also experiences a magnetic force. Current is a collection of many charged particles in motion, so the resultant force exerted by the magnetic field in the wire is the sum of the individual forces exerted on all the charged particles making up the current. The force exerted on the particles is transmitted to the wire when the particles collide with the atoms making up the wire. Slide 24 The force on a current-carrying conductor can be demonstrated by hanging a wire between the poles of a magnet. Slide 25 Equation: l is the length of the wire in the magnetic field. is the angle between the length of the wire (or the direction of the current) and the magnetic field. The direction of the magnetic force is found using the right hand rule. Fingers in the direction of I. Palm in direction of B. Thumb points in direction of F B. Slide 26 A current consists of charge carriers q moving with velocity v. Slide 27 Magnetic field around a long, straight current-carrying wire Slide 28 Forces Between Two Current-Carrying Wires Currents traveling in the same direction result in an attractive force acting between the two wires. Currents traveling in opposite directions through two wires produce a repulsive force between the two wires. Slide 29 Force between two parallel wires: o =4 x 10 -7 Tm/A l = length of conducting wire d = distance between wires Notice that opposites ( and x) attract and unlike ( and or x and x) repel. Slide 30 Motion of a Charged Particle in a Uniform Magnetic Field When a charged particle traveling with velocity v enters a uniform magnetic field perpendicular to the magnetic field, the particle moves in a circle in a plane perpendicular to the magnetic field. The particle moves in a circle because the magnetic force F B is at right angles to v and B and has a constant magnitude qvB. As the force deflects the particle, the directions of v and F B change continuously. Slide 31 Because F B always points toward the center of the circle, it changes only the direction of the velocity and does not affect the magnitude of the velocity. Motion of a charged particle under the action of a magnetic field alone is always motion with constant speed. The right hand rule can be used to determine the direction of the force acting on the charged particle. Because the particle moves under the influence of a constant force that is always at right angles to the velocity of the particle, the path is a circle of constant speed v. Slide 32 The inward directed magnetic force F B provides the centripetal force F C to keep the particle traveling in a circular path. Slide 33 Magnetic Field of a Current- Carrying Wire A current-carrying wire produces a magnetic field and can be detected by a compass needle placed near the wire. When no current is in the wire, all needles point in the direction of the Earths magnetic field. When the wire carries a strong, steady current, the needles deflect in directions tangent to the circle around the wire, pointing in the direction of the magnetic field B due to the wire. Slide 34 A current-carrying wire produces a magnetic field and can be detected by a compass needle placed near the wire. When no current is in the wire, all needles point in the direction of the Earths magnetic field. When the wire carries a strong, steady current, the needles deflect in directions tangent to the circle around the wire, pointing in the direction of the magnetic field B due to the wire. If the current is reversed, the needles reverse directions. Slide 35 Right hand rule for determining the direction of the magnetic field around a current carrying wire: if the wire is grasped in the right hand with the thumb in the direction of the current I, the fingers will curl around the wire in the direction of the magnetic field B. The magnetic field lines form concentric circles around the wire. Slide 36 The magnitude of B is the same everywhere on a circular path centered on the wire and lying in a plane perpendicular to the wire. Slide 37 The magnetic field strength increases as the current I increases. The magnetic field strength decreases as the distance from the wire increases. Equation: where r is the distance from the wire to the location of the o =4 x 10 -7 Tm/A magnetic field Slide 38 Current Loops and Solenoids The right hand rule can also be applied to find the direction of the magnetic field of a current-carrying loop. No matter where on the loop you apply the right hand rule, the field within the loop points in the same direction. Slide 39 If a long, straight wire is bent into a coil of several closely spaced loops, the resulting device is called a solenoid. Slide 40 Solenoids produce a strong magnetic field by combining several loops. The solenoid has many applications because it acts as a magnet when it carries a current. The magnetic field inside a solenoid increases with the current and the number of coils per unit length. The magnetic field of a solenoid can be increased by inserting an iron rod through the center of the coil; this device is often called an electromagnet. The magnetic field that is induced in the iron rod adds to the magnetic field of the solenoid, creating a more powerful magnet. Slide 41 In a car or truck, the starter solenoid helps to start the vehicle. The starter solenoid receives a large electric current from the battery and a small electric current from the ignition switch. When the ignition switch is turned on (when the key is turned to start the car), the small electric current forces the starter solenoid to close a pair of heavy contacts, thus relaying the large electric current to the starter motor. If a starter solenoid receives insufficient power from the battery, it will fail to start the motor, and may produce a rapid 'clicking' or 'clacking' sound. This can be caused by a low or dead battery, by corroded or loose connections in the cable, or by a broken or damaged positive (red) cable from the battery. Slide 42 Any of these will result in some power to the solenoid, but not enough to hold the heavy contacts closed, so the starter motor itself never spins, and the engine is not rotated and does not start. Slide 43 Magnetic field inside a solenoid: o =4 x 10 -7 Tm/A The quantity is the number of turns per unit length l : Magnetic field B inside a solenoid: