7 Magnetic Flux, F: The number of magnetic (flux) field lines which pass through a given cross-sectional area AUnits:F webersB TeslaA area m2angle formed between B and the normal to the loop (area vector A)The area vector A is perpendicular to the surface A and has a magnitude equal to the area A.
8 Example The magnetic flux through the loop is FB = BA cos q The induced emf ise = - d/dt (BA cos q)
9 The magnetic flux can be changed by: Changing the orientation of the wire loop in which the current is to be induced (movement).Changing the strength of the magnetic field (change current of wire that causes the field).Changing the area of the coil.
10 1. MovementWhen a wire is moved in a constant magnetic field, the wire “feels” a changed magnetic field and current is induced.
11 1. Change Caused by Movement -Sliding Conducting Bar (Motional EMF) emf = - B Lv sinqL: length of the wireq: angle between v and B
12 Sliding Conducting Bar Induced emf :Induced Current:
13 Sliding Conducting Bar A bar moving through a uniform field and the equivalent circuit diagramAssume the bar has zero resistanceThe work done by the applied force appears as internal energy in the resistor R
14 Sliding Conducting Bar and Energy The applied force does work on the conducting bar to move charges through a magnetic fieldThe change in energy of the system during some time interval must be equal to the transfer of energy into the system by workThe power input is equal to the rate at which energy is delivered to the resistor
20 Faraday’s ExperimentA primary coil is connected to a switch and a batteryThe wire is wrapped around an iron ringA secondary coil is also wrapped around the iron ringThere is no battery present in the secondary coilThe secondary coil is not directly connected to the primary coil
21 Faraday’s ExperimentAt the instant the switch is closed, the galvanometer (ammeter) needle deflects in one direction and then returns to zeroWhen the switch is opened, the galvanometer needle deflects in the opposite direction and then returns to zeroThe galvanometer reads zero when there is a steady current or when there is no current in the primary circuit
22 Faraday’s ExperimentAn electric current can be induced in the secondary circuit by changing the magnetic fieldThe induced current exists only while the magnetic field is changingNote: the flux must be changing
24 QuestionIn the “flying ring” demo, how was the magnetic field “felt” by the copper ring changed?Answer: AC current
25 3. When B is constant and A (area) is changing.
26 Ways of Inducing an emf The magnitude of B can change with time The area enclosed by the loop can change with timeThe angle q between B and the normal to the loop can change with timeAny combination of the above can occur
27 Applications of Faraday’s Law -GFI (Ground Fault Interuptor) A GFI protects users of electrical appliances against electric shock by triggering a circuit breakerWhen the currents in the wires are in opposite directions, the flux is zeroWhen the return current in wire 2 changes, the flux is no longer zeroAn emf results which can be trigger a circuit breaker.
28 Applications of Faraday’s Law – Pickup Coil of an Electric Guitar The coil is placed near the vibrating string and causes a portion of the string to become magnetizedWhen the string vibrates at the same frequency, the magnetized segment produces a changing flux through the coilThe induced emf is fed to an amplifier