Download
1 / 22
E N D
Faraday’s Law of Induction • (a) When a magnet is moved toward a loop of wire connected to asensitive ammeter, the ammeter deflects as shown, indicating that a current is inducedin the loop. (b) When the magnet is held stationary, there is no induced current in theloop, even when the magnet is inside the loop. (c) When the magnet is moved away • from the loop, the ammeter deflects in the opposite direction, indicating that theinduced current is opposite that shown in part (a). Changing the direction of themagnet’s motion changes the direction of the current induced by that motion
Faraday’s experiment. When the switch in the primary circuit isclosed, the ammeter in the secondary circuit deflects momentarily. The emf induced inthe secondary circuit is caused by the changing magnetic field through the secondary coil
Conclusion • a current is set up eventhough no batteries are present in the circuit • an electric current canbe induced in a circuit (the secondary circuit in our setup) by a changing magnetic field. • an induced emf is produced in the secondary circuit by the changing magnetic field.
Faraday’s law of induction • The emf induced in a circuit is directly proportional to the time rate of change ofthe magnetic flux through the circuit.
A conducting loop that encloses an area A in thepresence of a uniform magneticfield B. The angle between B andthe normal to the loop is θ
The induced emf can be expressed as • From this expression, we see that an emf can be induced in the circuit in several ways: • The magnitude of B can change with time. • The area enclosed by the loop can change with time. The angle θ between B and the normal to the loop can change with time. • Any combination of the above can occur.
Some Applications of Faraday’s Law • The ground fault interrupter (GFI) is an interesting safety device that protects users ofelectrical appliances against electric shock. • Another interesting application of Faraday’s law is the production of sound in an electric guitar
Electric guitar (a) In an electric guitar, a vibrating magnetized string induces an emf in apickup coil. (b) The pickups (the circles beneath the metallic strings) of this electricguitar detect the vibrations of the strings and send this information through an amplifier and into speakers. (A switch on the guitar allows the musician to select whichset of six pickups is used.)
Motional emf • motional emf is the emf induced in a conductor moving through a constant magnetic field.
A straight electrical conductor of length ! Movingwith a velocity v through a uniform magnetic field B directedperpendicular to v. Due to the magnetic force on electrons, theends of the conductor become oppositely charged. This establishesan electric field in the conductor. In steady state, the electric andmagnetic forces on an electron in the wire are balanced
(a) A conducting bar sliding with a velocity v alongtwo conducting rails under theaction of an applied force Fapp. Themagnetic force FB opposes themotion, and a counterclockwise current I is induced in the loop.(b) The equivalent circuit diagramfor the setup shown in part (a).
The condition for equilibrium requires that a potential difference is maintained between the ends of the conductor as long as the conductor continues to move through the uniform magnetic field. If the direction of the motion is reversed, the polarity of thepotential difference is also reversed
Because the area enclosed by the circuit at any instant is lx, where x is the positionof the bar • Using Faraday’s law, and noting that x changes with time at a rate dx/dt = v, we findthat the induced motional emf is, the magnetic flux through that area is
the power delivered by the applied force • We will see that this power input is equal to the rate at which energyis delivered to the resistor
Lenz’s Law • The induced current in a loop is in the direction that creates a magnetic field thatopposes the change in magnetic flux through the area enclosed by the loop • Consequence Faraday’s law indicates that the induced emf and the change in flux have opposite algebraic signs
(a) As the conducting bar slides on the two fixed conducting rails, the magnetic flux due to the externalmagnetic field into the page through the area enclosed by the loop increases in time. By Lenz’s law, the induced current must be counterclockwise so as toproduce a counteracting magntic field directed out of the page. (b) Whenthe bar moves to the left, the induced current must be clockwise.
(a) When the magnet is moved toward the stationary conductingloop, a current is induced in the direction shown. The magnetic field lines shownare those due to the bar magnet. (b) This induced current produces its ownmagnetic field directed to the left that counteracts the increasing external flux. Themagnetic field lines shown are those due to the induced current in the ring.(c) When the magnet is moved away from the stationary conducting loop, a currentis induced in the direction shown. The magnetic field lines shown are those due tothe bar magnet. (d) This induced current produces a magnetic field directed to theright and so counteracts the decreasing external flux. The magnetic field linesshown are those due to the induced current in the ring
A loop enclosing an area A and containing N turns,rotating with constant angular speed ω in a magnetic field. Theemf induced in the loop varies sinusoidally in time.
