Lecture 17 Chapter 33 Physics II Faraday s Law Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii
Electromagnetic induction We saw that a magnetic field could be produced with an electric current. The question arose as to whether electric current could be produced from a magnetic field. El. current Magn. field curious El. current Magn. field This discovery changed the world. It allowed making electricity to power industries.
Electromagnetic induction By experimenting Faraday concluded that a changing magnetic field can produce an electric current, which is called an induced current. The process is called electromagnetic induction. I When a bar magnet is pushed into a coil of wire, it causes a momentary deflection of the current meter needle. Holding the magnet inside the coil has no effect. A quick withdrawal of the magnet deflects the needle in the other direction. A changing something (magnetic field?) induces an EMF " " I
To write an expression for an EMF, we need to introduce the magnetic flux (it is very similar to the electric flux) Magnetic Flux
The Area Vector (recall) Let s define an area vector to be a vector in the direction of, perpendicular to the surface, with a magnitude A equal to the area of the surface. Vector has units of m 2. Slide 33-44
Magnetic Flux θ The magnetic flux measures the amount of magnetic field passing through a loop of area A if the loop is tilted at an angle from the field: In the case when magnetic field is not uniform and a surface is not flat, than the magnetic flux is The SI unit of magnetic flux is the weber: 1 weber = 1 Wb = 1 T m 2
ConcepTest Magnetic Flux The metal loop is being pulled through a uniform magnetic field. Is the magnetic flux through the loop changing? A) yes B) no B=const A=const Theta=const, So the flux is const
ConcepTest Magnetic Flux II The metal loop is rotating in a uniform magnetic field. Is the magnetic flux through the loop changing? A) yes B) no B=const A=const Theta=changes, So the flux is NOT const
Now, after introducing the magnetic flux, we can write the Faraday s Law Faraday s Law
Faraday s Law Now with the definition of flux, we can write mathematically what Faraday saw experimentally Faraday s law of induction: the emf induced in a circuit is equal to the rate of change of magnetic flux through the circuit: (It turns out that something is the magnetic flux) So we can induce EMF by changing: B, θ, A: ) Spinning a loop θ a loop is shrunk
Lenz s Law The minus sign gives the direction of the induced emf. To avoid dealing with this minus, we will calculate EMF in two steps: 1) 2) Apply Lenz s Law i.e. Any system doesn t like changes It opposes to a growing flux And Supports a dying flux
Lenz s Law (example) Pushing the bar magnet into the loop causes the magnetic flux to increase in the upward direction. To oppose the change in flux, which is what Lenz s law requires, the loop itself needs to generate an downward-pointing magnetic field. The induced current ceases as soon as the magnet stops moving. has CW direction
Example (Lenz s Law) The current in the straight wire is decreasing. I has CW direction
ConcepTest The current in the straight wire is increasing. Which is true? Lenz s law A) There is a clockwise induced current in the loop. B) There is a counterclockwise induced current in the loop C) There is no induced current in the loop. 1. The wire s B field is into the screen and increasing. 2. To oppose the increase in flux, the field of the induced current must point out of the screen. 3. From the right-hand rule, an inward field needs a ccw current. has CCW direction
ConcepTest Loop and Wire II What is the induced current if the wire loop moves in the direction of the yellow arrow? 1) clockwise 2) counterclockwise 3) no induced current The magnetic flux through the loop is not changing as it moves parallel to the wire. Therefore, there is no induced current. I = const
Faraday s Law for a U-shaped rail/rod system Let s apply Faraday s law for a conducting rod sliding on a U-shaped conducting rail. B is perpendicular to the plane of the rail. We can find the induced emf and current by using Faraday s law and Ohm s law: The EMF induced in the loop is: The induced current flows through the loop: Direction of the induced current: has CCW direction
ConcepTest The induced emf around this loop is Faraday s Law A) 200 V B) 20 V C) 2 V D) 0.5 V E) 0.2 V
What you should read Chapter 33 (Knight) Sections 33.3 33.4 33.5
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