PHYSICS 1444-001 Fall 2012 Lecture 15 Electromagnetic Induction and Faraday s Law
A current can be produced by a changing magnetic field First shown in an experiment by Michael Faraday Induced emf A primary coil is connected to a battery. A secondary coil is connected to an ammeter. The purpose of the secondary circuit is to detect current that might be produced by the magnetic field 2
He found no evidence when there was a steady current in the primary circuit, but did see a current induced when the switch was turned on or off. When the switch is closed, the ammeter deflects in one direction and then returns to zero When the switch is opened, the ammeter deflects in the opposite direction and then returns to zero Faraday s experiment used a magnetic field that was changing because the current producing it was changing. Therefore, a changing magnetic field induces an emf. 3
Faraday s Conclusions An electrical current is produced by a changing magnetic field The secondary circuit acts as if a source of emf were connected to it for a short time It is customary to say that an induced emf is produced in the secondary circuit by the changing magnetic field 4
Magnetic Flux The emf is actually induced by a change in the quantity called the magnetic flux rather than simply by a change in the magnetic field Magnetic flux is defined in a manner similar to that of electrical flux Magnetic flux is proportional to both the strength of the magnetic field passing through the plane of a loop of wire and the area of the loop 5
Magnetic Flux is proportional to both the strength of the magnetic field passing through the plane of a loop of wire and the area of the loop The loop of wire is in a uniform magnetic field B The loop has an area A The flux is defined as Φ B = B A = B A cos θ θ is the angle between B and the normal to the plane. SI units of flux are T m² = Wb (Weber) 6
The magnetic flux is proportional to the total number of lines passing through the loop 7
Magnetic Flux When the field is perpendicular to the plane of the loop, as in a, θ = 0 and Φ B = Φ B, max = BA When the field is parallel to the plane of the loop, as in b, θ = 90 and Φ B = 0 The flux can be negative, for example if θ = 180 The value of the magnetic flux is proportional to the total number of lines passing through the loop 8
The induced emf in a wire loop is proportional to the rate of change of magnetic flux through the loop. Magnetic flux: Unit of magnetic flux: weber, Wb: 1 Wb = 1 T m 2.
Electromagnetic Induction An Experiment When a magnet moves toward a loop of wire, the ammeter shows the presence of a current (a) When the magnet is held stationary, there is no current (b) When the magnet moves away from the loop, the ammeter shows a current in the opposite direction (c) If the loop is moved instead of the magnet, a current is also detected 10
Electromagnetic Induction Results of the Experiment A current is set up in the circuit as long as there is relative motion between the magnet and the loop The same experimental results are found whether the loop moves or the magnet moves The current is called an induced current because is it produced by an induced emf 11
Faraday s Law and Electromagnetic Induction The instantaneous emf induced in a circuit equals the time rate of change of magnetic flux through the circuit If a circuit contains one tightly wound loop and the flux changes by Φ B during a time interval t, the average emf induced is given by Faraday s Law: B t 12
Faraday s Law and Electromagnetic Induction If a circuit contains N tightly wound loops and the flux changes by Φ during a time interval t, the average emf induced is given by Faraday s Law: N t B The change in the flux, Φ, can be produced by a change in B, A or θ since Φ B = B A cos θ 13
Magnetic flux will change if the area of the loop changes: 14
Magnetic flux will change if the angle between the loop and the field changes: 15
Faraday s Law and Lenz Law The negative sign in Faraday s Law is included to indicate the polarity of the induced emf, which is found by Lenz Law The polarity of the induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loop That is, the induced current tends to maintain the original flux through the circuit 16
Applications of Faraday s Law Electric Guitar A vibrating string induces an emf in a coil A permanent magnet inside the coil magnetizes a portion of the string nearest the coil As the string vibrates at some frequency, its magnetized segment produces a changing flux through the pickup coil The changing flux produces an induced emf that is fed to an amplifier 17
Application of Faraday s Law Motional emf A straight conductor of length l moves perpendicularly with constant velocity through a uniform field The electrons in the conductor experience a magnetic force F = q v x B The electrons tend to move to the lower end of the conductor 18
As the negative charges accumulate at the base, a net positive charge exists at the upper end of the conductor As a result of this charge separation, an electric field is produced in the conductor Charges build up at the ends of the conductor until the downward magnetic force is balanced by the upward electric force There is a potential difference between the upper and lower ends of the conductor 19
The potential difference between the ends of the conductor can be found by V = B l v The upper end is at a higher potential than the lower end A potential difference is maintained across the conductor as long as there is motion through the field If the motion is reversed, the polarity of the potential difference is also reversed 20
Motional emf in a Circuit Assume the moving bar has zero resistance As the bar is pulled to the right with velocity v under the influence of an applied force, F, the free charges experience a magnetic force along the length of the bar This force sets up an induced current because the charges are free to move in the closed path 21
Motional emf in a Circuit The changing magnetic flux through the loop and the corresponding induced emf in the bar result from the change in area of the loop The induced, motional emf, acts like a battery in the circuit Bv and I Bv R 22
QUICK QUIZ 1 As an airplane flies due north from Los Angeles to Seattle, it cuts through Earth's magnetic field. As a result, an emf is developed between the wing tips. Which wing tip is positively charged? 23
QUICK QUIZ 1 ANSWER The left wing tip on the west side of the airplane. The magnetic field of the Earth has a downward component in the northern hemisphere. As the airplane flies northward, the right-hand rule indicates that positive charge experiences a force to the left side of the airplane. Thus, the left wing tip becomes positively charged and the right wing tip negatively charged. 24
Lenz Law Revisited Moving Bar As the bar moves to the right, the magnetic flux through the circuit increases with time because the area of the loop increases The induced current must be in a direction such that it opposes the change in the external magnetic flux The flux due to the external field is increasing into the page 25
The flux due to the external field is increasing into the page The flux due to the induced current must be out of the page Therefore the current must be counterclockwise when the bar moves to the right 26
The bar is moving toward the left The magnetic flux through the loop is decreasing with time The induced current must be clockwise to produce its own flux into the page 27
Lenz Law Revisited, Conservation of Energy Assume the bar is moving to the right Assume the induced current is clockwise The magnetic force on the bar would be to the right The force would cause an acceleration and the velocity would increase This would cause the flux to increase and the current to increase and the velocity to increase This would violate Conservation of Energy and so therefore, the current must be counterclockwise 28
Lenz Law, Moving Magnet Example A bar magnet is moved to the right toward a stationary loop of wire (a) As the magnet moves, the magnetic flux increases with time The induced current produces a flux to the left, so the current is in the direction shown (b) 29
Lenz Law, Final Note When applying Lenz Law, there are two magnetic fields to consider The external changing magnetic field that induces the current in the loop The magnetic field produced by the current in the loop 30
QUICK QUIZ 2 A bar magnet is falling through a loop of wire with constant velocity with the north pole entering first. Viewed from the same side of the loop as the magnet, as the north pole approaches the loop, the induced current will be in what direction? (a) clockwise (b) zero (c ) counterclockwise (d) along the length of the magnet 31
QUICK QUIZ 2 ANSWER (c). In order to oppose the approach of the north pole, the magnetic field generated by the induced current must be directed upward. An induced current directed counterclockwise around the loop will produce a field with this orientation along the axis of the loop. 32