Physics Week 5(Sem. 2) Name Chapter Summary Magnetism Magnetic Fields Permanent magnets have long been used in navigational compasses. The needle in a compass is supported to allow it to freely rotate in a plane. The needle will rotate allowing one side to point north and the other end to point south. Like electrical charges and their fields, magnetic fields exert forces on one another. For magnets, like poles repel and opposite poles attract. Unlike electric charges, north and south can not be isolated from one another. So no one has found a south pole, without a north pole. Even when a larger magnet is made smaller the smaller pieces each have a north and south pole. Magnetic fields have both magnitude and 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. Magnetic field lines can be drawn around a magnet to show direction. The magnetic field at any point is tangent to the magnetic field line at that point. And the strength of the magnetic field is proportional to the number of lines per unit area that passes through a surface oriented perpendicular to the lines. Magnetic field lines are closer together at the ends of the magnet where the field is stronger, this occurs at the poles. They always originate in the north pole and end in the south pole. Geomagnetism The geographic north pole varies from the magnetic north pole slightly. This point also varies slightly with time so the angle the compass deviates from the geographic north pole is called the angle of declination. Currently, NYC is about 12 o west, meaning the compass points 12 o west of the geographic north pole. Force of a Magnetic field on a Charge When a charge is placed in an electric field, the charge experiences an electric force and a magnetic force so long as: 1. The charge must be moving, no magnetic charges work on stationary charges. 2. The velocity of the moving charge must have a component that is perpendicular to the direction of the magnetic field. Ms. N. May
Look at figure 21.6 for a visual. The test charge (q o ) is moving with a velocity of v through a magnetic field. The vector of the magnetic field is labeled B, it is assumed to be constant in magnitude and direction. If the charge moves parallel or antiparallel then the charge experiences no magnetic field. If, the charge moves perpendicular to the field the charge experiences maximum possible magnetic force (F max ). If it moves with some angle θ only the velocities perpendicular component factors into the magnetic force (less than F max ). The force (F) is perpendicular to the plane that B and v are in, as seen in the figure. The Right Hand Rule (#1) can be used. The RHR 1 is to extend your right hand so the fingers point along the direction of the magnetic field B and the thumb points along the velocity of the charge v. The palm of the hand then faces in the direction of the magnetic force F that acts on the positive charge. If the charge is negative instead of positive then the force is in the opposite direction. The magnetic force can contribute to the net force on an object and thus cause the object to accelerate. Definition of the Magnetic Field The magnitude of a magnetic force (through a magnetic field) has been found to be directly proportional to the charge and to the component of the velocity that is perpendicular to the magnetic field. sin The unit of the magnetic field strength is Ns/Cm, this unit is called the tesla (T). Often the tesla can be written as 1 N/Am. The strength of the magnetic field near the earth s surface is approximately 1x10 4 T. Thus the unit gauss (not SI) is often used, where 1 gauss = 1x10 4 T. Motion in a Magnetic Field For a charged particle in an electric field the particle will move parallel to the electric field or sideways in the figure (as seen in 21.10). For a charged particle in a magnetic field (as pictured), the particle is deflected upwards. Applying the RHR 1 the velocity enters from the left, the field points into the page thus the magnetic field is up. For magnetism, the force is always perpendicular to the field. But for electricity, the force is always parallel (or antiparallel) to the field. Therefore, the work done by each field is different. Because the electric field exerts a force in the direction of the displacement, the electric field does work on the charged particle. Since the electric field can do work, it can change the kinetic energy of the particle. However, since the magnetic force is always perpendicular to the motion of the charged particle it never has displacement in the same direction. Thus the magnetic force cannot do work and cannot change the kinetic energy of the charged particle. The magnetic force can still alter the direction of the motion of the charged particle. The Circular Trajectory Considering a special case, of a charged particle with a velocity that is perpendicular to a uniform magnetic field, to fully understand that the magnetic field does not do work. The magnetic force moves the charged particle in a circular path. Meaning when the positively changed particle is at a point 1, the magnetic force F is perpendicular to the velocity v and points directly upwards (as seen in the picture). This force causes the trajectory to bend upward. When the particle reaches point 2, the magnetic force still remains perpendicular to the velocity, but is not directed to the left in the drawing. The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path. Recalling Centripetal Force F=mυ 2 /r, so qυb= mυ 2 /r. Thus r is This result shows that the radius of the circle is inversely proportional to the magnitude of the magnetic field, with stronger fields producing tighter circular paths. Ms. N. May
Ms. N. May
Ms. N. May
Ms. N. May
Ms. N. May
Name: 4121-1 - Page 1 1) The diagram below shows a bar magnet. Which arrow best represents the direction of the needle of a compass placed at point A? 2) A student sprinkled iron filings around a bar magnet and observed that the filings formed the pattern shown below. The magnetic field is strongest at point A B C D
3) Which diagram below best represents the magnetic field near a bar magnet? 4121-1 - Page 2 5) The diagram below shows electron e about to enter the region between the poles of two magnets. Upon entering the region between the poles, the moving electron will experience a magnetic force directed toward the south pole out of the page into the page toward the north pole 6) The diagram below shows the lines of magnetic force between two north magnetic poles. 4) The diagram below represents the magnetic lines of force around a bar magnet. At which point is the magnitude of the magnetic field strength of the bar magnet the greatest? A B C D At which point is the magnetic field strength greatest? A B C D 7) The diagram below shows a proton moving with velocity v about to enter a uniform magnetic field directed into the page. As the proton moves in the magnetic field, the magnitude of the magnetic force on the proton is F. If the proton were replaced by an alpha particle under the same conditions, what would be the magnitude of the magnetic force on the alpha particle? 4F 2F F
8) Which diagram best represents magnetic flux lines around a bar magnet? 4121-1 - Page 3 11) Which diagram best represents the magnetic field near the poles of a horseshoe magnet? 9) In the diagram below, a wire carrying an electron current into the page, as denoted by X, is placed in a magnetic field. 12) The diagram below represents a conductor carrying a current in which the electron flow is from left to right. The conductor is located in a magnetic field which is directed into the page. The magnetic field exerts a force on the wire toward point A B C D 10) The diagram below represents the magnetic field near point P. The direction of the magnetic force on the conductor will be toward the bottom of the page toward the top of the page into the page out of the page If a compass is placed at point P in the same plane as the magnetic field, which arrow represents the direction the north end of the compass needle will point?
4121-1 - Page 4 13) The diagram below represents an electron beam in a vacuum. The beam is emitted by cathode C, accelerated by anode A, and passes through electric and magnetic fields. In which direction will the force of the magnetic field act on the electron beam? toward the bottom of the page toward the top of the page out of the page into the page 14) A magnetic field will be produced by stationary ions stationary protons moving electrons moving neutrons Questions 44 through 48 refer to the following: The diagram below represents a helium ion with a charge of +2 elementary charges moving toward point A with a constant speed (v) of 2.0 meters per second perpendicular to a uniform magnetic field between the poles of a magnet. The strength of the magnetic field is 0.10 weber per square meter. 15) The helium ion is replaced by an electron moving at the same speed. Compared to the magnitude of the force on the helium ion, the magnitude of the force on the electron is the same greater less 16) If the strength of the magnetic field and the speed of the helium ion are both doubled, the force on the helium ion will be the same doubled quadrupled halved 17) The direction of the magnetic force on the helium ion is toward point B D A C 18) The magnitude of the magnetic force exerted on the helium ion is 3.2 x 10-20 N 0.20 N 6.4 x 10-20 N 0.10 N 19) If the polarity of the magnet is reversed, the magnitude of the magnetic force on the helium ion will increase decrease remain the same 20) The field around a permanent magnet is caused by the motions of neutrons electrons protons nucleons
21) In the diagram below, what is the direction of the magnetic field at point A? Questions 17 through 21 refer to the following: 4121-1 - Page 5 The diagram below represents an electron moving at 2.0 x 10 6 meters per second into a magnetic field which is directed into the paper. The magnetic field has a strength of 2.0 newtons per ampere-meter. toward the bottom of the page toward the top of the page to the left to the right 22) Which diagram best represents the magnetic field around a material of high permeability placed between unlike magnetic poles? 24) Which vector best indicates the direction of the force on the electron? 23) In which diagram below is the magnetic flux density at point P greatest? 25) If the strength of the magnetic field were increased, the force on the electron would increase remain the same decrease 26) The electron is replaced with a proton moving with the same velocity. Compared to the magnitude of the force on the electron, the magnitude of the force on the proton would be greater less the same 27) What is the magnitude of the force on the electron? 6.4 x 10-13 newton 4.0 x 10 6 newtons 8.0 x 10 6 newtons 6.4 x 10 6 newtons 28) If the velocity of the electron were increased, the force on the electron would increase remain the same decrease 29) If a charged particle moving through a magnetic field experiences a magnetic force, the angle between the magnetic field and the force exerted on the particle is 180D 0D 45D 90D
30) In the diagram below, A, B, C, and D are points in the magnetic field near a current-carrying loop. At which points is the direction of the magnetic field into the page? 4121-1 - Page 6 32) An electron traveling at a speed (v) in the plane of this paper enters a uniform magnetic field. Which diagram best represents the condition under which the electron will experience the greatest magnetic force as it enters the magnetic field? A and D C and D B and C A and B 31) Which diagram below best represents a magnetic field? 33) Which diagram best represents a magnetic field between two magnetic poles?
34) A wire 0.10 meter long is pushed through a magnetic field of strength 4.0 newtons per ampere-meter in a direction perpendicular to the field. If the speed of the wire is 2.0 meters per second, what is the magnitude of the induced voltage across the ends of the wire? 0.50 volt 2.0 volts 0.20 volt 0.80 volt 35) As two parallel conductors with currents in the same direction are moved apart, their force of repulsion decreases repulsion increases attraction decreases attraction increases 36) Which diagram best represents the magnetic field between two magnetic north poles? 38) Each diagram below represents a cross section of a long, straight, current-carrying wire with the electron flow into the page. Which diagram best represents the magnetic field near the wire? 4121-1 - Page 7 37) A magnetic force is experienced by an electron moving through a magnetic field. If the electron were replaced by a proton traveling at the same velocity, the magnitude of the magnetic force experienced by the proton would be twice as great zero the same half as great 39) Which diagram best represents the lines of magnetic flux between the ends of two bar magnets?
40) A particle with a charge of 2 x 10-6 coulomb crosses a uniform magnetic field perpendicularly. The particle experiences a force of 1 x 10-3 newton. If the particle has a speed of 1 x 10 6 meters per second, the magnitude of the field strength is 2 x 10 3 weber/meter 2 5 x 10-4 weber/meter 2 5 x 10-1 weber/meter 2 2 x 10-3 weber/meter 2 4121-1 - Page 8 43) Which arrow in the diagram below represents the direction of the flux inside the bar magnet? 41) The diagram below represents a conductor carrying an electron current in magnetic field B. The direction of the magnetic force on the conductor is D C B A out of the page into the page toward the bottom of the page toward the top of the page 42) The diagrams below show cross sections of conductors with electrons flowing into or out of the page. In which diagram below will the magnetic flux density at point A be greater than the magnetic flux density at point B? 44) The diagram below shows an end view of a current-carrying wire between the poles of a magnet. The wire is perpendicular to the magnetic field. If the direction of the electron flow is out of the page, which arrow correctly shows the direction of the magnetic force F acting on the wire? 45) The existence of a magnetic field around a current-carrying conductor can be demonstrated by placing the conductor near a battery a compass needle an electroscope a pith ball
46) The diagram below shows a loop of wire between the poles of a magnet. The plane of the loop is parallel to the magnetic field. If an electron flow is established in the direction shown in the loop, in which direction will a magnetic force be exerted on segment AB? 4121-1 - Page 9 47) A volt is to electric potential as a tesla is to charge density magnetic flux density electric field intensity electrical energy 48) The wire loop shown below has a clockwise electron current. toward the top of the page out of the page into the page toward the bottom of the page What is the direction of the magnetic field at point P? out of the page into the page to the right to the left
1. Which combination of units can be used to express magnetic field strength? (1) kg s C (2) N C (3) N m C (4) kg m C (5) kg m s C 5. A particle with a charge of +2 10 7 C and a mass of 4 10 4 kg experiences an acceleration of 3.2 m/s 2 due a magnetic field of 8 T. The velocity of the particle may be (1) 800 m/s parallel to the magnetic field. (2) 400 m/s perpendicular to the magnetic field. (3) 800 m/s perpendicular to the magnetic field. (4) 800 m/s at an angle of 30º to the magnetic field. (5) 400 m/s at an angle of 30º to the magnetic field. 2. Which of the following explains why a magnetic field does no work on a moving charged particle? (1) The magnetic force depends on the direction of motion of the particle. (2) The magnetic force is conservative. (3) The magnetic force depends on the speed of the particle. (4) The magnetic force is always perpendicular to the direction of motion. (5) There is always an electric field that cancels the work done by the magnetic field. 3. A particle with a charge of +3 µc and mass 2 10 8 kg enters a 0.01 T magnetic field with a velocity of 5 10 5 m/s perpendicular to the field. The acceleration of this particle due to the magnetic force is (1) 9.5 10 5 m/s 2 (4) 2.5 10 5 m/s 2 (2) 1.5 10 5 m/s 2 (5) 7.5 10 5 m/s 2 (3) 4.5 10 5 m/s 2 4. A particle with a mass of 1.2 10 5 kg experiences an acceleration of 2 10 3 m/s 2 as it enters a magnetic field of 3 T with a velocity of 4 10 5 m/s at an angle of 30º with the magnetic field. The magnitude of the charge on the particle is (1) 0.04 µc (4) 0.4 µc (2) 80 µc (5) 4 µc (3) 40 µc 6. 7. In the figure above, what is the direction of the magnetic force vector? (1) To the right (2) Out of the page (3) To the left (4) Into the page (5) Upward in the plane of the page In the figure above, what is the direction of the particle's velocity? (1) Into the page (2) Out of the plane of the page (3) Upward, in the plane of the page (4) To the left (5) To the right
Base your answers to questions 8 and 9 on the following. Traveling at an initial speed of 1.2 10 6 m/s, a particle (mass = 6 10 10 kg, charge = 1.0 10 10 enters a region of uniform magnetic field with a strength of 300 T at an angle of 30º to the field. 8. What is the magnitude of the acceleration of the particle? (1) 3.0 10 17 m/s 2 (4) 7.2 10 7 m/s 2 (2) 3.0 10 7 m/s 2 (5) 9.0 10 3 m/s 2 (3) 1.8 10 2 m/s 2 9. What is the speed of the particle after 1 s? (1) 3.0 10 6 m/s (4) 5.4 10 6 m/s (2) 6.0 10 5 m/s (5) 4.2 10 6 m/s (3) 1.2 10 6 m/s 10. In order for a magnetic field to exert a force on an object, which of the follow can be true? I. The object is charged. II. The object is moving parallel to the field. III. The object is moving perpendicular to the field. (1) I and II only (4) I only (2) II only (5) I and III only (3) III only