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Electric and Magnetic Fields An electric field surrounds any stationary electric charge The region of space surrounding a moving charge includes a magnetic field In addition to the electric field A magnetic field also surrounds any material with permanent magnetism Both fields are vector fields 1 Magnetic Poles Every magnet, regardless of its shape, has two poles Called north and south poles Poles exert forces on one another Similar to the way electric charges exert forces on each other Like poles repel each other N-N or S-S Unlike poles attract each other N-S 2 Magnetic Poles, cont The poles received their names due to the way a magnet behaves in the Earth's magnetic field If a bar magnet is suspended so that it can move freely, it will rotate The magnetic north pole points toward the earth's north geographic pole This means the earth's north geographic pole is a magnetic south pole Similarly, the earth's south geographic pole is a magnetic north pole 3 Magnetic Poles, final The force between two poles varies as the inverse square of the distance between them A single magnetic pole has never been isolated In other words, magnetic poles are always found in pairs There is some theoretical basis for the existence of monopoles single poles 4 Magnetic Fields A vector quantity r Symbolized by B Direction is given by the direction a north pole of a compass needle points in that location magnetic field lines can be used to show how the field lines, as traced out by a compass, would look 5 magnetic field lines , Bar Magnet Example The compass can be used to trace the field lines The lines outside the magnet point from the North pole to the South pole 6 magnetic field lines , Bar Magnet Iron filings are used to show the pattern of the magnetic field lines The direction of the field is the direction a north pole would point 7 magnetic field lines , Unlike Poles Iron filings are used to show the pattern of the magnetic field lines The direction of the field is the direction a north pole would point Compare to the electric field produced by an electric dipole 8 magnetic field lines , Like Poles Iron filings are used to show the pattern of the magnetic field lines The direction of the field is the direction a north pole would point Compare to the electric field produced by like charges 9 Definition of Magnetic Field The magnetic field at some point in space can be defined in terms of the r magnetic force, FB The magnetic force will be exerted on a charged particle moving with a velocity, r v 10 Characteristics of the Magnetic Force The magnitude of the force exerted on the particle is proportional to the charge, q, and to the speed, v, of the particle When a charged particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero 11 Characteristics of the Magnetic Force, cont When the particle's velocity vector makes any angle 0 with the field, the magnetic force acts in a direction perpendicular to both the speed and the field The magnetic force is perpendicular to the r r plane formed by v and B 12 Characteristics of the Magnetic Force, final The force exerted on a negative charge is directed opposite to the force on a positive charge moving in the same direction If the velocity vector makes an angle with the magnetic field, the magnitude of the force is proportional to sin 13 More About Direction The force is perpendicular to both the field and the velocity Oppositely directed forces exerted on oppositely charged particles will cause the particles to move in opposite directions 14 Force on a Charge Moving in a Magnetic Field, Formula The characteristics can be summarized in a vector equation r r r FB = qv B r FB is the magnetic force q is the charge r v is the velocity of the moving charge r B is the magnetic field 15 Units of Magnetic Field The SI unit of magnetic field is the Tesla (T) N s T = C m The cgs unit is a Gauss (G) 1 T = 104 G 16 Directions Right Hand Rule #1 Depends on the right-hand rule for cross products The fingers point in the direction of the velocity The palm faces the field Curl your fingers in the direction of field The thumb points in the direction of the cross product, which is the direction of force For a positive charge, opposite the direction for a negative charge 17 Direction Right Hand Rule #2 Alternative to Rule #1 Thumb is the direction of the velocity Fingers are in the direction of the field Palm is in the direction of force On a positive particle Force on a negative charge is opposite You can think of this as your hand pushing the particle 18 Problem 22.1. Determine the initial direction of the deflection of charged particles as they enter the magnetic fields as shown in Figure P22.1. 19 More About Magnitude of the Force The magnitude of the magnetic force on a charged particle is FB = |q| v B sin is the angle between the velocity and the field The force is zero when the velocity and the field are parallel or antiparallel = 0 or 180o The force is a maximum when the velocity and the field are perpendicular = 90o 20 Differences Between Electric and Magnetic Fields Direction of force The electric force acts parallel or antiparallel to the electric field The magnetic force acts perpendicular to the magnetic field Motion The electric force acts on a charged particle regardless of its velocity The magnetic force acts on a charged particle only when the particle is in motion and the force is proportional to the velocity 21 More Differences Between Electric and Magnetic Fields Work The electric force does work in displacing a charged particle The magnetic force associated with a steady magnetic field does no work when a particle is displaced This is because the force is perpendicular to the displacement 22 Work in Fields, cont The kinetic energy of a charged particle moving through a constant magnetic field cannot be altered by the magnetic field alone When a r charged particle moves with a velocity v through a magnetic field, the field can alter the direction of the velocity, but not the speed or the kinetic energy 23 Notation Note The dots indicate the direction is out of the page The dots represent the tips of the arrows coming toward you The crosses indicate the direction is into the page The crosses represent the feathered tails of the arrows 24 Charged Particle in a Magnetic Field Consider a particle moving in an external magnetic field with its velocity perpendicular to the field The force is always directed toward the center of the circular path The magnetic force causes a centripetal acceleration, changing the direction of the velocity of the particle 25 Force on a Charged Particle Using Newton's Second Law, you can equate the magnetic and centripetal forces: mv 2 F = ma qvB = r mv Solving for r: r = qB r is proportional to the linear momentum of the particle and inversely proportional to the magnetic field and the charge 26 More About Motion of Charged Particle The angular speed of the particle is v qB = = r m The angular speed, , is also referred to as the cyclotron frequency The period of the motion is 2 r 2 2 m = = T = v qB 27 Problem 22.13. The picture tube in a television uses magnetic deflection coils rather than electric deflection plates. Suppose an electron beam is accelerated through a 50.0-kV potential difference and then through a region of uniform magnetic field 1.00 cm wide. The screen is located 10.0 cm from the center of the coils and is 50.0 cm wide. When the field is turned off, the electron beam hits the center of the screen. What field magnitude is necessary to deflect the beam to the side of the screen? Ignore relativistic corrections. 28 Motion of a Particle, General If a charged particle moves in a magnetic field at some arbitrary angle with respect to the field, its path is a helix Same equations apply, with 2 2 v = vy + vz 29 (i) A charged particle is moving perpendicular to a magnetic field in a circle with a radius r. The magnitude of the magnetic field is increased. Compared with the initial radius of the circular path, is the radius of the new path 100% 1. 2. 3. smaller, larger, or equal in size? 0% r, al le rg e 0% r r, o si eq ua li n ze ? sm la 30 An identical particle enters the field, with perpendicular to , but with a higher speed v than the first particle. Compared with the radius of the circle for the first particle in the same magnetic field, is the radius of the circle for the second particle 100% 1. 2. 3. smaller, larger, or equal in size? 0% r, al le rg e 0% r r, o si eq ua li n ze ? sm la 31 Charged Particle Moving in Electric and Magnetic Fields In many applications, the charged particle will move in the presence of both magnetic and electric fields In that case, the total force is the sum of the forces due to the r individualrfields r r In general: F = qE + qv B This force is called the Lorenz force It is the vector sum of the electric force and the magnetic force 32 Velocity Selector Used when all the particles need to move with the same velocity A uniform electric field is perpendicular to a uniform magnetic field 33 Velocity Selector, cont When the force due to the electric field is equal but opposite to the force due to the magnetic field, the particle moves in a straight line This occurs for velocities of value v=E/B 34 Velocity Selector, final Only those particles with the given speed will pass through the two fields undeflected The magnetic force exerted on particles moving at speed greater than this is stronger than the electric field and the particles will be deflected upward Those moving more slowly will be deflected downward 35

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