General Physics II. Electromagnetic Induction and Electromagnetic Waves

Transcription

1 General Physics II Electromagnetic Induction and Electromagnetic Waves 1

2 Induced emf We have seen that an electric current produces a magnetic field. Michael Faraday demonstrated that a magnetic field can be used to generate, or induce, an emf, which in turn can produce a current in a conductor. The process of inducing an emf with a magnetic field is called electromagnetic induction. The best way to demonstrate electromagnetic induction is to conduct experiments (as Faraday did). 2

3 Electromagnetic Induction Experiments 3

4 Induced emf Our observations indicate that a current, and hence an emf, is induced in a conducting loop when: The loop moves relative to a steady non-uniform magnetic field. The faster the motion, the greater the magnitude of the induced emf. The direction of the induced emf reverses when the direction of motion reverses. If there is no motion, there is no emf. The magnetic field changes within the stationary loop. The faster the change, the greater the emf. The direction of the induced emf reverses when the sign of the change in the field reverses. If there is no change, there is no emf. 4

5 Motional emf Consider a conductor of length l that moves in a uniform magnetic field B with velocity v that is perpendicular to the field. We assume by convention that the charge carriers in the conductor are positive. As the conductor moves, the charges move with it. The movement of the charges within the magnetic field produces a magnetic force, which drives the charges along the length of the conductor (in this case, upward). 5

6 Motional emf The positive charges accumulate at the top, leaving a net negative charge at the bottom. This creates an electric field that exerts a downward electric force on the charges in opposition to the magnetic force. Eventually, the forces become equal in magnitude and the net force on a charge carrier is then zero. There is no further charge accumulation. At this point, F = E qe = F = B qvb 6 E = vb.

7 Motional emf Note that the conductor is very much like a battery. A nonelectrostatic force (the magnetic force) causes charge separation leading to an electric field and potential difference. The work done per unit charge by the magnetic force is the emf of the conductor. This emf is equal to the potential difference between the top and bottom ( terminals ) of the conductor: E =Δ V= El. E= vlb. (Motional emf) (Valid for a straight conductor with velocity perpendicular to the magnetic field.) 7 7

8 Motional emf in a Circuit If a straight wire slides over a C- shaped conducting rail in a magnetic field, the motional emf of the sliding wire will cause a current to be established in the circuit. The current is given by I = ΔV = E = vlb, R R R where R is the total circuit resistance. The current in the moving wire causes a magnetic force in the direction opposite its velocity. Thus, an external force F is necessary to pull prevent the wire from slowing down and stopping. F mag F pull 8

9 Workbook, Chapter 25, Questions 1, 2, 3 9

10 Generator A generator converts mechanical energy into electric energy. One of the most common methods is via the motional emf produced by a coil rotating in a steady magnetic field. 10

11 Magnetic Flux We have seen that moving a magnet into or out of a stationary conducting loop and moving the loop into or out of a steady magnetic field generates an induced current in the loop. It turns out that a current can be induced in a conducting loop in other ways, such as: Rotating the loop within a steady magnetic field (as we have seen in the operation of a generator); Changing the area of the loop in a steady magnetic field; Immersing the loop in a time-varying magnetic field (e.g., produced by solenoid whose current changes with time). All cases in which a current is induced in a conducting loop (due to the presence of an induced emf) can be described by changes is a single quantity called the magnetic flux. 11

12 Magnetic Flux The magnetic flux is proportional to the number of magnetic field lines going through a loop. The greater the (i) magnetic field and (ii) area of the loop exposed to the field, the greater the magnetic flux. 12

13 Magnetic Flux The magnetic flux Φ is defined as Φ = ABcos θ, where A is the area of the loop, B is the magnetic field, and θ is the angle between the axis of the loop and the magnetic field. 13

14 Workbook: Chapter 25, Question 4 14

15 Lenz Law The utility of the concept of magnetic flux is that it allows us to make a simple statement that encompasses all the magnetically-induced current experiments we have seen: A current is induced in a closed conducting loop whenever there is a change in the magnetic flux through the loop. Lenz s law tells us the direction in which the induced current will flow. Lenz s law states that the induced current flows in a direction such that its own magnetic field opposes the change in magnetic flux that produced the current in the first place. 15

16 Applying Lenz s Law B induced Induced current 16

17 Workbook: Chapter 25, Question 5 17

18 Faraday s Law In our induction experiments, we saw that the more rapidly the magnetic flux changes through a conducting loop, the greater the induced current. The greater induced current is due to a greater induced emf. Faraday s Law gives us a quantitative statement of the relationship between the induced emf and the rate at which the magnetic flux changes. Faraday s Law states that the induced emf in a loop is equal to the magnitude of the rate of change of the magnetic flux through the loop. The emf is in the same direction as the induced current given by Lenz s law. Mathematically, Faraday s law for a single loop is written as E = ΔΦ. Δ t For an N-turn coil, we have E = N ΔΦ Δt per turn. 18

19 Workbook: Chapter 25, Question 6, 7 19

20 Textbook: Chapter 25, Problem 12 20

21 Eddy Currents If the magnetic flux changes through a bulk conductor (e.g., a sheet of metal), currents will be induced. These currents are not confined to single loops. Rather they are distributed over the region in which the magnetic flux changes. Such currents are called eddy currents. Consistent with Lenz s law, the magnetic force acting on the conductor due to the eddy currents opposes the motion of the conductor. This is useful for magnetic braking. 21