Physics 154 Midterm 2 Notes Chapter 21 PDF

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CHAPTER 21 NOTES 21.1 Magnetic Fields ● Permanent magnets have been used in navigational compasses ● When the compass is placed on a horizontal surface, the needle rotates until one end points approximately to the north ○ The end of the needle that points north is labeled the north magnetic pole and the opposite end is the south magnetic pole ● Magnets can exert forces on each other. Magnetic forces between north and south poles ○ Like poles repel each other, and unlike poles attract ● Magnets and electric charges are similar and different ○ It is possible to separate positive from negative electric charges and produce isolated charges of either kind ○ No one has found a magnetic monopole (an isolated north or south pole) ■ Any attempt to separate north and south poles by cutting a bar magnet in half fails, because each piece becomes a smaller magnet with its own north and south poles ● There is a magnetic field surrounding a magnet ○ Like the electric field, the magnetic field has both a magnitude and a direction ● The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point ● As is the case with electric field lines, the magnetic field at any point is tangent to the magnetic field line at that point ● The strength of the field is proportion to the number of lines per unit area that passes through a surfaces oriented perpendicular to the lines ● Thus, the magnetic field is stronger in regions where the field lines are relatively close together and weaker where they are relatively far apart ● The field linens in the gap between the poles of the horseshoe magnet are nearly parallel and equally spaced - indicating that the magnetic field there is approximately constant ● The angle of declination is the angle that compass needle deviates ● The angle that the magnetic field makes with respect to the surface at any point is known as the angle of dip 21.2 The Force That a Magnetic Field Exerts on a Moving Charge ● When a charge is placed in an electric field it experiences an electric force ● When a charge is placed in a magnetic field, it also experiences a force ● The magnetic force may contribute to the net force that causes an object to accelerate. Thus, when present, the magnetic force must be included in Newton’s second law ○ The following conditions must be met for a charge to experience a magnetic force when placed in a magnetic field ■ 1) The charge must be moving, because magnetic force acts on a stationary charge

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2) The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field ● If the charge moves parallel or antiparallel to the field, the charge experiences no magnetic force ● If the charge moves perpendicular to the field, the charge experiences the maximum possible force As an aid in remembering the direction of the force, it is convenient to use the Right Hand Rule Number 1 (RHR-1) ○ Extend the right hand so the fingers point along the direction of the magnetic field B and the thumb points along the velocity of the charge. The palm of the hand then faces in the direction of the magnetic force that acts on a positive charge ■ It is as if the open palms of the right hand pushes on the positive charge in the direction of the magnetic force ● If the moving charge is negative instead of positive, the direction of the magnetic force is opposite to that predicted by the RHR-1 With magnetic field, the test charge is moving, and the force depends not only onn the charge q but also on the velocity component v sin theta that is perpendicular to the magnetic field ○ Definition of magnetic field

■ One tesla is the strength of the magnetic field in which a unit test charge, traveling perpendicular to the magnetic field at a speed of one meter per second, experiences a force of one newton. ○ Tesla is often written as 1 T = 1 N/(A*m) ■ 1 gauss = 10^-4 tesla

1. Suppose that you accidentally use your left hand, instead of your right hand, to determine the direction of the magnetic force that acts on a positive charge moving in a magnetic field. Do you get the correct answer? (a) Yes, because either hand can be used (b) No, because the direction you get will be perpendicular to the correct direction (c) No, because the direction you get will be opposite to the correct direction

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(C) No, because the direction you get will be opposite to the correct direction - The right hand rule states that-"Extend the right hand so the fingers point along the direction of the magnetic field B and the thumb points along the velocity V of the charge. The palm of the hand then faces in the direction of the magnetic force F that acts on a positive charge".

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When we use the left hand, the configuration of out hands are different, so we will get a direction that will be opposite to the direction of the original force.

Two particles, having the same charge but different velocities, are moving in a constant magnetic field (see the drawing, where the velocity vectors are drawn to scale). Which particle, if either, experiences the greater magnetic force? (a) Particle 1 experiences the greater force, because it is moving perpendicular to the magnetic field. (b) Particle 2 experiences the greater force, because it has the greater speed. (c) Particle 2 experiences the greater force, because a component of its velocity is parallel to the magnetic field. (d) Both particles experience the same magnetic force, because the component of each velocity that is perpendicular to the magnetic field is the same.

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(d)Both particles experience the same magnetic force, because the component of each velocity that is perpendicular to the magnetic field is the same.

3. A charged particle, passing through a certain region of space, has a velocity whose magnitude and direction remain constant. (a) If it is known that the external magnetic field is zero everywhere in this region, can you conclude that the external electric field is also zero? (b) If it is known that the external electric field is zero everywhere, can you conclude that the external magnetic field is also zero?

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a) yes b) no When the particle travels through the space, if its velocity and direction remain the same, means that the net force acting on it is zero. If the electric field is present in the region, there ought to be a force from the electric field and net force cannot be zero because there is no other source of force. Since the net force is zero, means that the net electric field is zero. If a particle has a velocity parallel to the direction of electric field, the force due to magnetic field will be zero, so if just magnetic field is present, we cannot comment anything about the magnetic field in the region.

21.3 The Motion of a Charged Particle in a Magnetic Field ● Comparing particle motion in electric and magnetic fields ○ As the charge moves upward, the direction of the magnetic force changes, always perpendicular to both the magnetic field and the velocity ○ A charged particle traveling in a magnetic field experiences a magnetic force that is always perpendicular to the field. The force applied by an electric field is always parallel (or antiparallel) to the field direction. ■ Because of the difference in the way that electric and magnetic field exert forces, the work done on a charged particle by each field is different ● The work done on on a charged particle moving through electric and magnetic fields ○ An electric field applies a force to a positively charged particle, and the path of the particle bends in the direction of the force ■ The force does work on the particle

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The work increases the kinetic energy and thus the speed of the particle ○ In contrast, the magnetic force always acts in a direction that is perpendicular to the motion of the charge ■ Consequently, the displacement of the moving charge never has a component in the direction of the magnetic force ● As a result, the magnetic force cannot do work and change the kinetic energy of the charged particle ○ Thus the speed of the particle does not change, although the force does alter the direction of the motion The circular trajectory ○ The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path ○ The magnitude of the magnetic force is given by

21.4 The Mass Spectrometer ● With a speed v, the ions pass through a hole in the plate and enter a region of constant magnetic field where they are deflected in semicircular paths ● The mass of each ion reaching the detector is proportional to B^2

○ 21.5 The Force on a Current in a Magnetic Field ● A charge moving through a magnetic field can experience a magnetic force ○ Since an electric current is a collection of moving charges, a current in the presence of a magnetic field can also experience a magnetic force

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○ Direction of magnetic force is given by RHR-1

21.6 The Torque on a Current-Carrying Coil ● If a loop of wire is suspended properly in a magnetic field, the magnetic force produces a torque that tends to rotate the loop ● When there is a current in the loop, the loop rotates because magnetic forces act on the vertical sides ● Torque is maximum when the normal to the plan of the loop is perpendicular to the field ● Torque is zero when the normal is parallel to the field ● When a current-carrying loop is placed in a magnetic field, the loops tends to rotate such that its normal becomes aligned with the magnetic field ○ A current loop behaves like a magnet suspended in a magnetic field, since a magnet rotates to align itself with the magnetic field ● Calculating net torque ○

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In this result, the product Lw has been replaced by the area A of the loop. If the wire is wrapped to form a coil containing N loops, each of area A, the force on each side is N times larger and the torque becomes proportionally greater The quantity NIA is known as the magnetic moment of the coil, its unit is ampere*meter^2 ● The greater the magnetic moment of a current-carrying coil, the greater is the torque that the coil experiences when placed in a magnetic field

21.7 Magnetic Field Produced by Currents ● A current-carrying wire also produces a magnetic field of its own ● A long, straight wire

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When a current is present, the compass needles point in a circular pattern about the wire ■ The pattern indicates that the magnetic field lines produced by the current are circles centered on the wire ■ If the direction of the current is reversed, the needles also reverse their directions, indicating that the direction of the magnetic field has reversed The direction of the field can be obtained by using Right-Hand Rule Number 2 ■ RHR-2 ● Curl the fingers of the right hand into the shape of a half-circle. Point the thumb in the direction of the conventional current I, and the tips of the fingers will point in the direction of the magnetic field Magnetic field produced by infinitely long, straight wire

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u0= permeability of free space and its value is The magnetic field becomes stronger nearer the wire, where r is smaller ○ Field lines near the wire are closer together than those located farther away where the field is weaker ○ The magnetic field that surrounds a current-carrying wire can exert a force on a moving charge ○ The magnetic field that one current creates can exert a force on another nearby current ○ *In this example the currents in the wires and the distance between them are known; therefore, the magnetic force that one wire exerts on the other can be calculated. If, instead, the force and the distance were known and the wires carried the same current, that current could be calculated. A loop of wire ○ Center of a circular loop

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A solenoid ○ Long coil of wire in the shape of a helix ○ The field inside the solenoid and away from its ends is nearly constant in magnitude and directed parallel to the axis

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■ n is number of turns per unit length Often referred to as electromagnets

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Several advantages ● Strength of the magnetic field can be altered by changing the current and/or the number of turns per unit length ● The north and south poles can be readily switched by reversing the current

21.9 Magnetic Materials ● Ferromagnetism ○ Field that surrounds the loop is created by the charges moving in the wire ○ Motion responsible for magnetism is that of the electrons within the atoms of the material ■ Electron orbiting the nucleus behaves like an atomic-sized loop of current that generates a small magnetic field ■ Each electron possess a spin that also gives rise to a magnetic field ● The net magnetic field created by the electrons within an atom is due to the combine fields created by their orbital and spin motions...