# College Physics B - PHY2054C

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1 Force on a Torque on a College - PHY2054C & 09/29/2014 My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building

2 Outline Force on a Torque on a 1 Force on a Torque on a 2 3 4

3 Force on a Torque on a Force on a 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

4 Force on a Torque on a Force on a 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 B F on wire = I L B If B is at an angle θ with the wire: F on wire = I L B sin θ

5 Force on a Torque on a F = q E + q v B 1 Electric Force depends on the electric field. 2 Force depends on the magnetic field and the particle s velocity.

6 Force on a Torque on a 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. What is the effect of the magnetic force? A The two wires attract each other. B The two wires repel each other. C There is no effect. D I don t know. (Not for credit)

7 Force on a Torque on a Review Question 2 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 the point P in the picture, 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

8 Force on a Torque on a Review Question 2 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 the point P in the picture, 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. Right-Hand Rule I P

9 Force on a Torque on a Review Question 3 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 the point P in the picture, 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

10 Force on a Torque on a Review Question 3 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 the point P in the picture, 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 Right-Hand Rule I

11 Force on a Torque on a Review Question 4 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. What is the effect of the magnetic force? A The two wires attract each other. B The two wires repel each other. C There is no effect. D I don t know.

12 Force on a Torque on a Review Question 4 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. What is the effect of the magnetic force? A The two wires attract each other. B The two wires repel each other. C There is no effect. D I don t know.

13 Force on a Torque on a Torque on a 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.

14 Force on a Torque on a Torque on a 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 sin θ

15 Force on a Torque on a Question 5 The figure shows a current loop in a magnetic field. Is there a torque on the loop and, if so, in what direction? A There is a torque that tends to rotate the loop in direction (a), clockwise. B There is a torque that tends to rotate the loop in direction (b), counterclockwise. C The torque is zero.

16 Force on a Torque on a Question 5 The figure shows a current loop in a magnetic field. Is there a torque on the loop and, if so, in what direction? A There is a torque that tends to rotate the loop in direction (a), clockwise. B There is a torque that tends to rotate the loop in direction (b), counterclockwise. C The torque is zero.

17 Outline Force on a Torque on a 1 Force on a Torque on a 2 3 4

18 Force on a Torque on a 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

19 Force on a Torque on a The magnetic force exerted on a moving charged particle is dependent on its velocity. Differs substantially from gravitational and electrical forces. Observer 1 (A) sees magnetic force. Observer 2 (B) sees an electric force. Special relativity solves the dilemma. Chapter 27

20 Force on a The magnetosphere is the region around Earth where charged particles from the solar wind are trapped. Torque on a

21 Force on a Charged particles are trapped in areas called the Van Allen Belts, where they spiral around the magnetic field lines. Torque on a

22 Force on a Charged particles are trapped in areas called the Van Allen Belts, where they spiral around the magnetic field lines. Torque on a Two doughnut-shaped zones km (protons) 2 20,000 km (electrons)

23 Aurora Borealis Force on a Torque on a 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.

24 Aurora Borealis Force on a Torque on a

25 Outline Force on a Torque on a 1 Force on a Torque on a 2 3 4

26 Force on a Torque on a Connection between Electricity and Magnetism Sources of Electric Fields Electric Charge Sources of Fields

27 Electric Fields Force on a Torque on a Capacitor Michael Faraday ( ) Static Point Charges

28 Force on a Torque on a Connection between Electricity and Magnetism Sources of Electric Fields Electric Charge Sources of Fields Moving Electric Charge

29 Force on a Torque on a Electromagnetism Christian Oersted ( ) Field around a currentcarrying wire is fairly weak

30 Force on a Torque on a A coil concentrates and strengthens the field Field around a currentcarrying wire is fairly weak Electromagnetism

31 Force on a Torque on a Connection between Electricity and Magnetism Sources of Electric Fields Electric Charge Changing Fields Sources of Fields Moving Electric Charge

32 Force on a Why does the power company place large electric devices on the utility poles near homes or on the ground near neighborhoods? Torque on a

33 Force on a Why does the power company place large electric devices on the utility poles near homes or on the ground near neighborhoods? Torque on a

34 Force on a Torque on a Michael Faraday attempted to observe an induced electric field. He did not use a light bulb. A If the bar magnet is stationary, the current and the electric field are both zero. B If the bar magnet was in motion, a current was observed. : phet.colorado.edu/sims/faradays-law/faradays-law_en.html

35 Force on a Torque on a Another Faraday A solenoid is positioned near a loop of wire with the light bulb. Now a current is passed through the solenoid by connecting it to a battery. 1 When the current through the solenoid is constant, there is no current in the wire. 2 When the switch is opened or closed, the bulb does light up.

36 Force on a Torque on a Question 6 What is the conclusion from? It shows that an electric current is produced in the wire loop only when A the battery is directly connected to the light bulb. B the magnetic field at the loop is constant. C the magnetic field at the loop is changing. D No electric current is produced. A magnetic field cannot produce an electric current to power the light bulb.

37 Force on a Torque on a Question 6 What is the conclusion from? It shows that an electric current is produced in the wire loop only when A the battery is directly connected to the light bulb. B the magnetic field at the loop is constant. C the magnetic field at the loop is changing. D No electric current is produced. A magnetic field cannot produce an electric current to power the light bulb. A changing magnetic field produces an electric field. It is called induced electric field. The phenomenon is called electromagnetic induction.

38 Force on a Torque on a Faraday developed a quantitative theory of induction now called : It uses the concept of magnetic flux that is similar to the concept of electric flux: Φ B = A B cos θ (θ = (normal vector, magnetic field))

39 Force on a Torque on a Faraday developed a quantitative theory of induction now called : Φ B = A B cos θ The unit of magnetic flux is the Weber (Wb) 1 Wb = 1 T m 2

40 Force on a Torque on a indicates how to calculate the potential difference that produces the induced current: E = Φ B t The magnitude of the induced emf equals the rate of change of the magnetic flux.

41 Example Force on a Torque on a A magnetic field B is constant and in a direction perpendicular to the plane of the rails and the bar. Assume the bar moves at constant speed: Φ B = B A = B w L Φ B t = E = B L w t = B L v I = B L v R

42 Example Force on a Torque on a A magnetic field B is constant and in a direction perpendicular to the plane of the rails and the bar. Assume the bar moves at constant speed: Φ B = B A = B w L Φ B t = E = B L w t = B L v I = B L v R

43 Example Force on a Torque on a A magnetic field B is constant and in a direction perpendicular to the plane of the rails and the bar. Assume the bar moves at constant speed: Φ B = B A = B w L Φ B t = E = B L w t = B L v I = B L v R

44 Force on a Torque on a

45 Force on a Torque on a The mechanical power put into the bar by the external agent is equal to the electrical power delivered to the resistor: Energy is converted from mechanical to electrical; total energy remains the same.

46 Force on a Torque on a Need to make the rate of change of the flux large enough to give a useful emf: Use rotational motion instead of linear motion. A permanent magnet produces a constant magnetic field in the region between its poles. The angle between the field and the plane of the loop changes as the loop rotates. If the shaft rotates with a constant angular velocity, the flux varies sinusoidally with time. Generator: phet.colorado.edu/en/simulation/generator

47 Outline Force on a Torque on a 1 Force on a Torque on a 2 3 4

48 Force on a Torque on a gives us an easy way to determine the sign of the induced emf. states that the magnetic field produced by an induced current always opposes any changes in the magnetic flux.

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