Welcome our newest concept… Magnetic Flux
Faraday’s Observations,1830 When a magnet moves toward a loop of wire, the ammeter shows the presence of a current When the magnet is held stationary, there is no current 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
Experimental Conclusions A current is set up in the circuit as long as there is relative motionbetween 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 since there is no power source. An EMF is actually induced by a change in the magnetic flux.
Faraday’s Law & Electromagnetic Induction The instantaneous emf induced in a circuit equals the time rate of change of magnetic flux through the circuit. EM induction refers to electricity deriving from magnetism whereas electromagnetism is the opposite.
Traffic light sensors There is an inductive loop at intersection of Ft Wash & Susquehanna.
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
Apnea Monitor The coil of wire attached to the chest carries an alternating current An induced emf produced by the varying field passes through a pick up coil When breathing stops, the pattern of induced voltages stabilizes and external monitors sound an alert
Applications of Faraday’s Law – Ground Fault Interrupters The ground fault interrupter (GFI) is a safety device that protects against electrical shock Wire 1 leads from the wall outlet to the appliance Wire 2 leads from the appliance back to the wall outlet The iron ring confines the magnetic field, which is generally 0 If a leakage occurs, the field is no longer 0 and the induced voltage triggers a circuit breaker shutting off the current
Faraday's Law is the basic principle behind the microphone. In a microphone there is a diaphragm, around which a coil is wrapped, which can move back and forth in response to sound waves. A stationary bar magnet, placed near the coil, induces current in the coil which can then be transmitted (with amplification) to the speaker.
Example i d w l A long wire carries current i a distance ‘d’ from a rectangular wire loop as shown above. Determine an expression for the flux through loop.
Negative sign explained in Faraday’s Law The negative sign in Faraday’s Law is included to indicate the polarity of the induced emf, which is found by Lenz’ Law:
i If i(t) = 3t +1, what was direction of induced current in loop as t increases? d w l
Lenz’s Law examples Determine direction of induced current in loop
Determine direction of induced current in loop as magnet approaches loop area.
I y Iinduced v (a)ccw (b)cw (c) no induced current x Example A conducting rectangular loop moves with constant velocity v in the -y direction and a constant current I flows in the +x direction as shown What is the direction of the induced current in the loop?
Generator A coil of wire turns in a magnetic field. The flux in the coil is constantly changing, generating an emf in the coil. • Converts mechanical energy to electrical energy
If loop is made to rotate at constant rate ω in uniform B, we have from Faraday’s Law:
(e)Motional EMF A straight conductor of length ℓ moves perpendicularly with constant velocity through a uniform field ℓ
A conducting bar is placed across conducting path and pulled to right with speed v as shown. As bar moves, a change in flux occurs which induces CCW current.
Also, a magnetic force on bar arises which acts as a resistance to the motion of the bar as it is pulled to the right
Lenz’ Law Revisited, Conservation of Energy Consequence Assume the induced current is clockwise instead… 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
example A metal rod of mass 0.22kg lies across two parallel conducting rails which sits on a tabletop as shown. The rod and rails have negligible resistance but significant friction where uk=0.20. A field of 0.80T points into page. A string pulls the rod to right at a constant speed of 1.8m/s.
a) Calculate the force needed to pull rod at constant speed. b) Calculate the energy dissipated in the resistor in 2.0s. c) Calculate the work done by string in 2.0s.
Example A conducting rod with mass m and length L moves on two frictionless parallel rails in the presence of a uniform magnetic field. The bar is given an initial velocity vi at time t=0. Calculate the velocity of the bar as a function of time. Bar will slow down due to resistive force.
The magnitude of the magnetic force is given by Now, using Newton's second law, we can write the net force on the conducting rod as
Eddy currents Eddy currents are small circular or swirling currents that arise in conductors like a sheet of metal.
Eddy currents lead to heat being generated in the conductor This is the basic principle behind induction stoves. Safe to touch unless you are metallic. Eddy currents are established in cookware causing metal to heat up.
Magnetic Braking Rollercoaster brakes Analog speedometers
The Lamar Advantage 4200 Elliptical Trainer by Star Trac will allow you to train smarter by delivering an effective full-body workout without the joint pounding stress associated with jogging. As you exercise, contoured urethane rollers glide smoothly on our dual-rail tracking system. By offering 16 intensity levels, theelectronically controlled magnetic brake (ECB) will continue to provide a challenge. Elliptical Machines
Transformers A transformer is a device used to change the voltage in a circuit. AC currents must be used. 75,000 V in the power lines 120 V in your house
Electrical Power Transmission When transmitting electric power over long distances, it is most economical to use high voltage and low current, which minimizes I2R power losses.
Induced E-fields Ampere's Lawhas shown us how currents, moving electric charges, can create magnetic fields. Faraday's Lawhas shown us how changing magnetic fields can induce an emf in a closed loop.
Consider a loop of wire outside of a solenoid. Current is flowing through solenoid from back to front where B-field from coils is into page. Side View Front View
If the current is dereased gradually, the magnetic field in the solenoid's core decreases and an emf & Iinduced will be induced in the wire loop (LENZ LAW).
The force that pushes the charges around the wire is F = qE, where E is the induced electric field.
E-fields produced by either static charge or induction both exert forces on charged particles, however, there is an important difference. Static E Induced E
Recall we previously learned that the potential difference between 2 points in a static field is given by:
However, in a changing B-field case… As charge makes journey around closed loop, it must be experiencing an emf, however, to interpret that as a changing potential, it doesn’t make sense. Why?
time B As magnetic field increases in time through loop, an electric field is generated
S N Consider B-field between pole of electromagnet. Assume B to be uniform at any instant over a circular radius R. The current in the windings of the electromagnet increase with time. Beyond the circular region (r > R), assume B=0. Find E at any distance r from the center. side view top view, looking down on N pole
E r r E