Physics 24100 Electricity & Optics Lecture 16 Chapter 28 sec. 1-3 Fall 2017 Semester Professor Koltick
Magnetic Flux We define magnetic flux in the same way we defined electric flux: φ e = n E da φ m = n B da S S S
Calculating Magnetic Flux If the surface is a plane over which the magnetic field is constant, then φ m = S n BdA = BA cos θ Units of magnetic flux: Webers 1 Wb = 1 T m 2
Faraday s Law of Magnetic Induction A change in magnetic flux through a conducting loop induces a current in the loop. What causes the charges in the conductor to move? An electromotive force, ℇ ℇ = dφ m dt Another way to think about it: Changing magnetic flux induces an electric field This changes the electric potential of the charge carriers
Demonstration When a bar magnet is moved in the vicinity of a loop of wire, the magnetic flux through the loop will change. A current is induced Faster motion induces a larger current. No current when the motion stops.
Lecture 16-2 Faraday s Experiments (1) When we move the north pole of the magnet toward the wire loop, we induce a positive current in the loop When we move the south pole of the magnet toward the loop, we induce a negative current in the loop 2
Lecture 16-3 Faraday s Experiments (2) Now let s point the north pole toward the loop but move away from the loop We get a negative current We turn the magnet around so that the south pole points toward the loop and move away from the loop We get a positive current 3
Lecture 16-4 Faraday s Experiments (3) We can create similar effects by placing a second loop near the first loop If a constant current is flowing through loop 1, no current will be induced in loop 2 If we increase the current inloop 1, we observe that a current is induced inloop 2 in the opposite direction 4
Lecture 16-5 Faraday s Experiments (4) Now if we have the current flowing in loop 1 in the same direction as before, and decrease the current as indicated below, we induce a current in loop 2, in the same direction as the current in loop 1 5
Lecture 16-10 Lenz s Law As the magnet moves toward the loop, the magnitude of the field increases in the direction pointing toward the north pole Lenz s law states that a current is induced in the loop that tends to oppose the change in magnetic flux This induced magnetic field then points in the opposite direction from the field from the magnet 10
Lecture 16-6 Induction Bar magnet approaches coil Current induced in coil S N v Reverse poles of magnet Current in opposite direction N S v Bar magnet stationary No induced current Coil approaches bar magnet Current induced in coil v S N N S What s in common?: Change of Magnetic flux = EMF!
Changes in Magnetic Flux The magnetic flux through a loop can change in various ways: The magnetic field could change The source of the magnetic field could move The loop could move in a non-uniform field The orientation of the loop could change Others? Examples
Lecture 16-7 Faraday s Law of Induction The magnitude of the induced EMF in conducting loop is equal to the rate at which the magnetic flux through the surface spanned by the loop changes with time. ε dφ B dt where B B nda S N Minus sign indicates the sense of EMF: Lenz s Law N
Lecture 16-8 Induced Electric Field from Faraday s Law EMF is work done per unit charge: ε W / q If work is done on charge q, electric field E must be present: ε E ds nc W q E ds nc Rewrite Faraday s Law in terms of induced electric field: E nc ds dφ dt This form relates E and B! B B Note that E ds 0 for E fields generated by charges at rest (electrostatics) since this would correspond to the potential difference between a point and itself. => Static E is conservative. The induced E by magnetic flux changes is non-conservative, E nc
Lecture 16-9 Conducting Loop in a Changing Magnetic Field Induced EMF has a direction such that it opposes the change in magnetic flux that produced it. approaching Magnetic moment created by induced currrent I repels the bar magnet. Force on ring is repulsive. moving away Magnetic moment created by induced currrent I attracts the bar magnet. Force on ring is attractive.
Lecture 16-11 Lenz s Law - Four Cases a) An increasing magnetic field pointing to the right induces a current that creates a magnetic field to the left b) An increasing magnetic field pointing to the left induces a current that creates a magnetic field to the right c) A decreasing magnetic field pointing to the right induces a current that creates a magnetic field to the right d) A decreasing magnetic field pointing to the left induces a current that creates a magnetic field to the left 11
Lecture 16-12 Faraday s and Lenz s Laws At 1, 3, and 5, B is not changing. So there is no induced emf. At 2, B is increasing into page. So emf is induced to produce a counterclockwise current. At 4, B in decreasing into page. So current is clockwise.
Lecture 16-14 Ways to Change Magnetic Flux B BAcos Changing the magnitude of the field within a conducting loop (or coil). Changing the area of the loop (or coil) that lies within the magnetic field. Changing the relative orientation of the field and the loop. motor generator
Lecture 16-15 Other Examples of Induction + - - + Switch has been open for some time: Nothing happening Switch is just closed: EMF induced in Coil 2 Switch is just opened: EMF is induced again + - Switch is just closed: EMF is induced in coil Back emf (counter emf)
Demonstration: The Electromagnetic Cannon An alternating voltage source produces a changing magnetic field in the solenoid. When the magnetic field increases, the induced current tries to oppose it The magnetic field induced in the loop will oppose changes in B v Attractive force Repulsive force The magnetic forces fling the ring. side view B ~
Lecture 16-17 Demo: Jumping Rings (2) 17
Lecture 16-18 Demo (2): Cylindrical Object Falling through a Pipe Object 18
Lecture 16-19 Demo: Magnet Falling through a Pipe S N N S B i B magnet 19
Lenz s Law Changing magnetic flux induces a current in a loop of wire. The induced current will create its own magnetic field. Lenz s Law: The induced magnetic field will oppose changes to the original magnetic field. If the flux is decreasing, the induced field will increase the flux will add to the applied field If the flux is increasing the induced field will be opposite the applied field