AP Physics ST Motional emf Lenz’s Law ireference.ca

Motional emf “Flying Conductor” Previously - – Consider the induced emf generated by a varying magnetic field passing through fixed conducting circuit. Now – – Consider the induced emf when a conductor moves through a fixed magnetic field. – Referred to as “motional emf” electron9.phys.utk.edu

Motional emf “Flying Conductor” Consider a conducting rod… – Length L – Moving with constant speed, v – Perpendicular to a uniform magnetic field, B, directed into the page. Using the RHR predict what will occur… electron9.phys.utk.edu

Motional emf “Flying Conductor” According to the RHR… – Positive charges experience a magnetic force directed up (negative charges down). – Top of rod becomes positively charged, bottom of rod becomes negatively charged. – Thus producing an electric field, E, directed down. electron9.phys.utk.edu FBFB

Motional emf “Flying Conductor” Magnitude of magnetic field… Due to the charge separation an electric field is created, directed down – Thus the electric force is directed down electron9.phys.utk.edu FBFB FEFE

Motional emf “Flying Conductor” Charge will continue to separate, the electric field will continue to build, until the magnetic force is balanced out by the electric force… Recall…

Motional emf “Flying Conductor” Simplified… But recall that the uniform electric field is related to the potential difference between the ends of the rod… The potential difference then between the ends of a rod of length L…

Motional emf “Flying Conductor” Potential difference is maintained only as long as there is motion of the conductor in the magnetic field … – If the direction of motion is reversed there is a change in polarity in the rod.

Motional emf “Flying Conductor” Because this potential difference is induced in the rod due to motion of the rod through the magnetic field we define the potential difference as: Motional emf…

Motional emf “Changing Flux” Consider pushing a conducting rod along conducting rails at a constant speed… – Notice the flux changes within the circuit loop. – Using Faraday’s Law of induction determine the magnitude of the induced emf.

Motional emf “Changing Flux” As the bar is pushed to the right a current is established within the closed loop circuit as before. According to Faraday’s Law…

Motional emf “Changing Flux” Faraday’s Law considers the rate of change of magnetic flux through the loop. One can see that the induced emf is directly proportional to the change in area…

Motional emf “Changing Flux” Magnetic field lines are passing through an area… Flux then results in… x

Motional emf “Changing Flux” The induced emf then is… Simplifying… Again we confirm Motional emf… v

Motional emf If the resistance R of the circuit is known then the magnitude of the current can then be determined using Ohm’s Law… – THIS leads to an understanding of how the induction brakes on the Tower of Doom work!

Energy Back to the circuit… – So, how can there be a current if there is no battery?? – If the laws of nature say that energy must be conserved, from where does the energy come?? We see that an applied force results in a current… F app

Energy The work done by the applied force must be proportional to the induced emf… The work done by the applied force must be equal to the energy dissipated across the resistor. F app

Energy How big is the applied force? Back to the RHR… 1.Apply RHR first time to establish the charge separation. 2.Apply RHR second time to establish the direction of the magnetic force acting on the rod. F app FBFB

Energy If the applied force is to move the rod at constant speed then the net force must equal zero. Therefore the applied force must be equal to the induced magnetic force. Recall… F app FBFB

Energy The work done by the applied force…

Energy The RATE of energy dissipation (power)… Recall… Power of motional emf…

Lenz’s Law Lenz’s Law – – The direction of the induced emf is such that the induced magnetic flux OPPOSES the change in external magnetic flux. – This observation affirms the conservation of energy.

Lenz’s Law As the bar moves to the right the external magnetic flux increases! Lenz’s Law identifies the direction of the induced current to be such that the magnetic flux IT produces opposes the CHANGE of the external magnetic flux.

Lenz’s Law External mag field INTO page. Induced mag field OUT OF page. As the conservation of energy drives this necessary observation we see that the induced current is counterclockwise.

Lenz’s Law Counter argument…If this were NOT true… – F app and F B would be in the same direction… – Net force means the bar would accelerate… – This would cause the area to increase more quickly… – Resulting in a greater current… – Producing a greater net force…increasing A even more quickly… – ULTIMATELY RESULTING IN…

Lenz’s Law … the total annihilation of the Death Star! cache.gawkerassets.com

Lesson Summary

Example #1: Serway 5 th ed A conducting rod of length L moves on two horizontal, frictionless rails. If a constant force of 1.00 N moves the bar at 2.00 m/s through a magnetic field B that is directed into the page a.what is the current through an 8.00 Ω resistor R? b.what is the rate at which energy is delivered to the resistor? c.what is the mechanical power delivered by the F app ? F app

Example #2 Determine the direction of the emf in the following situations: – N into loop – S out of loop – N out of loop – S into loop