College Physics B - PHY2054C. Magnetic Fields and Forces 09/24/2014. My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building.

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1 Motion of a d College - PHY2054C and 09/24/2014 My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building

2 Outline Motion of a d 1 2 Motion of a d

3 Right-Hand Rule Motion of a d Point the thumb of your right hand in the direction of the current: Your thumb will be parallel to the wire. Curling the fingers of your right hand around the wire gives the direction of the magnetic field.

4 Motion of a d Review Question 1 Two current-carrying wires are parallel as shown below; the current is the same in both wires. The current in both wires is flowing to the right. At a point midway between the wires, the direction of the net magnetic field is A to the right B to the left C into the screen D out of the screen E The field is zero. P

5 Motion of a d Review Question 1 Two current-carrying wires are parallel as shown below; the current is the same in both wires. The current in both wires is flowing to the right. At a point midway between the wires, the direction of the net magnetic field is A to the right B to the left C into the screen D out of the screen E The field is zero. P

6 Plotting Field Lines Motion of a d Field lines are three-dimensional. 1 A large dot ( ) indicates the tip of the vector when it points out of the plane. 2 A cross ( ) denotes the tail of the vector when it points into the plane.

7 Motion of a d Review Question 2 Two current-carrying wires are parallel as shown below; the currents are now in the opposite directions. At a point midway between the wires (point A), the direction of the net magnetic field is A to the right B to the left C into the screen D out of the screen E The field is zero.

8 Motion of a d Review Question 2 Two current-carrying wires are parallel as shown below; the currents are now in the opposite directions. At a point midway between the wires (point A), the direction of the net magnetic field is A to the right B to the left C into the screen D out of the screen E The field is zero.

9 Motion of a d s and The electric current can be modeled as a collection of positive electric charges. The charges would be moving with a velocity parallel to the current direction. The direction of the magnetic field is given by the right-hand rule. A positive charge moving to the left produces the same magnetic field as a negative charge moving to the right. Principle of Superposition The Principle of Superposition states the total magnetic field produced by two or more different sources is equal to the sum of the fields produced by each source individually.

10 Motion of a d Review Question 3 The current-carrying wire as shown below is bent into a loop. At any point in the wire loop, the direction of the net magnetic field is: A to the right B to the left C into the screen D out of the screen E The field is zero.

11 Motion of a d Review Question 3 The current-carrying wire as shown below is bent into a loop. At any point in the wire loop, the direction of the net magnetic field is: A to the right B to the left C into the screen D out of the screen E The field is zero.

12 Motion of a d Treat the loop as many small pieces of wire: Apply the right-hand rule to find the field from each piece of wire. Applying superposition gives the overall pattern shown on the right. At the center of the loop: B = µ 0 I 2R

13 Motion of a d Solenoids By stacking many loops close together, the field along the axis is much larger than for a sinle loop. A helical winding of wire is called a solenoid. More practical than stacking single loops.

14 Outline Motion of a d 1 2 Motion of a d

15 Motion of a d The magnetic force acts on individual charges. The force depends on the velocity, v, of the charge. If the charge is not moving, there is no magnetic force. If a positive charge, q, is moving with a given velocity in an external magnetic field, then the magnitude of the force on the charge is: F B = q v B F B = q v B sinθ The angle, θ, is the angle between the velocity and the magnetic field.

16 Motion of a d Right-Hand Rule II Direction of the Force Version 1: Point the fingers of your right hand in the direction of the velocity and curl them in the direction of the magnetic field. Your thumb then points in the direction of the force.

17 Motion of a d Right-Hand Rule II Direction of the Force Version 1: Point the fingers of your right hand in the direction of the velocity and curl them in the direction of the magnetic field. Your thumb then points in the direction of the force. Version 2: Point the thumb in the direction of the positive charge s velocity and the index finger in the direction of the magnetic field. Your middle finger will give you the direction of the force.

18 Motion of a d Lorentz Force The magnetic force ( Lorentz Force ) is always perpendicular to both the magnetic field and the particle s velocity. The right-hand rule applies to a positive charge. For a negative charge, reverse the direction of the force on the particle.

19 Motion of a d Lorentz Force The magnetic force ( Lorentz Force ) is always perpendicular to both the magnetic field and the particle s velocity. The right-hand rule applies to a positive charge. For a negative charge, reverse the direction of the force on the particle. Note that the magnetic force does not do work: W = F s = F s cosθ = 0, since the force is always perpendicular to the direction of the motion cos 90 = 0. The force does not change the kinetic energy, only the direction.

20 Motion of a d Question 4 An electric charge Q is located at a fixed position inside a magnetic field B. It feels A a force perpendicular to the magnetic field. B a force parallel to the magnetic field. C no force. D a torque around its axis.

21 Motion of a d Question 4 An electric charge Q is located at a fixed position inside a magnetic field B. It feels A a force perpendicular to the magnetic field. B a force parallel to the magnetic field. C no force. D a torque around its axis. Since the charge is not moving, there is no magnetic force.

22 Motion of a d Question 5 The figure shows in part A an electric charge q moving past a stationary bar magnet and in part B a bar magnet moving past a stationary electric charge. In which case will there be a magnetic force on the charge? A Only in A B Only in B C In both A and B D Neither in A nor in B

23 Motion of a d Question 5 The figure shows in part A an electric charge q moving past a stationary bar magnet and in part B a bar magnet moving past a stationary electric charge. In which case will there be a magnetic force on the charge? A Only in A B Only in B C In both A and B D Neither in A nor in B

24 Motion of a d Motion of a d in a Field Assume a charged particle moves parallel to the magnetic field as in the picture: The angle between the velocity and the field is zero. What is the force on the particle?

25 Motion of a d Motion of a d in a Field Assume a charged particle moves parallel to the magnetic field as in the picture: The angle between the velocity and the field is zero. F = 0, since sinθ = 0 What about the trajectory?

26 Motion of a d Motion of a d in a Field Assume a charged particle moves parallel to the magnetic field as in the picture: The angle between the velocity and the field is zero. F = 0, since sinθ = 0 The particle will not change its motion; it will continue to move parallel to the magnetic field.

27 Motion of a d Motion of a d in a Field Assume now a charged particle moves perpendicular to the magnetic field as in this picture: The angle between the velocity and the field is 90. F = q v B, since sinθ = 1 The particle will now move in a circle. The circle lies in the plane perpendicular to magnetic field ( circular motion ): F B = q v B = mv 2 r = mv q B r

28 Motion of a d Motion of a d in a Field Finally assume a charged particle moves neither parallel nor perpendicular to the magnetic field: The angle between the velocity and the field varies. The path of the particle is helical. The charged particle will spiral around the magnetic field lines.

29 Motion of a d Motion of a d in a Field The charged particle will spiral around the magnetic field lines: F B = q v B = mv 2 r = mv q B = p q B r

30 Outline Motion of a d 1 2 Motion of a d

31 Motion of a d An electric current is a collection of moving charges: A force acts on a current. F B = q v B = ( Q) v B Velocity of charge : v = L t : I = Q t

32 Motion of a d An electric current is a collection of moving charges: A force acts on a current. F B = q v B = ( Q) v B Velocity of charge : v = L t : I = Q t F B = ( Q) v B = ( Q) L t F on wire = I L B B If B is at an angleθ with the wire: F on wire = I L B sinθ

33 Motion of a d A magnetic field can produce a torque on a current loop: A On two sides, the current is parallel or antiparallel to the field, so the force is zero on those sides. The forces on sides 1 and 3 are in opposite directions and produce a torque on the loop.

34 Motion of a d A magnetic field can produce a torque on a current loop: A On two sides, the current is parallel or antiparallel to the field, so the force is zero on those sides. When the angle between the loop and field is θ, the torque is: τ = L/2 F τ = I L 2 B sinθ

35 Outline Motion of a d 1 2 Motion of a d

36 Motion of a d A mass spectrometer allows for the separation of ions according to their mass or charge. Ions enter spectrometer with some speed v. They pass into a region where magnetic field is perpendicular to velocity circles Measure v and B, then calculate q/m: r = mv q B

37 Outline Motion of a d 1 2 Motion of a d

38 Motion of a d The magnetic force exerted on a moving charged particle is dependent on its velocity. Differs substantially from gravitational and electrical forces. Observer 1 sees magnetic force. Observer 2 sees electric force. Special relativity solves the dilemma.

39 Outline Motion of a d 1 2 Motion of a d

40 Motion of a d The magnetosphere is the region around Earth where charged particles from the solar wind are trapped.

41 Motion of a d d particles are trapped in areas called the Van Allen Belts, where they spiral around the magnetic field lines.

42 Motion of a d d particles are trapped in areas called the Van Allen Belts, where they spiral around the magnetic field lines. Two doughnut-shaped zones km (protons) 2 20,000 km (electrons)

43 Aurora Borealis Motion of a d A colorful aurora results from the emission of light radiation after magnetospheric particles collide with atmospheric molecules. The aurora rapidly flashes across the sky, resembling huge wind-blown curtains glowing in the dark.

44 Aurora Borealis Motion of a d

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