3/1/13 Chapter 25: EM Induction and EM Waves Key Terms: Induced Induced emf current Flux Lenz s Law waves Photons EM Don t Copy This Last chapter we learned that a current can create a magnetic field. Once this was discovered, physicists began investigating the reverse: can magnetic fields create a current? Michael Faraday 1
Induced Current Faraday found that a current can be created in a coil of wire if and only if the magnetic field passing through the coil is changing. Motional emf Motional emf The magnetic force on the charge carriers in a moving conductor creates an electric field inside the conductor. The electric field creates an electric potential difference between the two ends of the moving conductor. The potential difference depends on the strength of the magnetic field, the wire s length, and on the wire s speed through the field. 2
Sample Problem #1 (ex. 25.1, page 819) A Boeing 747 aircraft with a wingspan of 65 m is cruising at 260 m/s over northern Canada, where the magnetic field of the earth (magnitude 5.0 x 10-5 T) is directed straight down. What is the potential difference between the tips of the wings? If the plane is flying east, which wing is positive? Stop to Think A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor? Induced Current The induced emf across a wire can create an induced current in a circuit. 3
Sample Problem #2 (ex. 25.5, page 827) The figure below shows a wire of resistance R sliding on a U-shaped conducting rail. Assume that the conducting rail is an ideal wire. Derive an expression for the current in the wire. Sample Problem #3 How much force must the wire be pulled with in order for it to slide along the conducting rail with a constant velocity? (Assume friction is negligible) 4
Magnetic Flux Magnetic flux is the amount of magnetic field that goes through a loop. The amount of field depends on the strength of the field and the effective area. Sample Problem #4 (ex. 25.2, page 823) At a particular location, the earth s magnetic field is 50 μt tipped at an angle of 60 below the horizontal. A 10 cm diameter circular loop of wire sits flat on a table. What is the magnetic flux through the loop? Lenz s Law Current is induced in a loop of wire when the magnetic flux through the loop changes. The direction of the induced current is such that the induced magnetic field opposes the change in the flux. 5
How Flux Can Change 1) The magnetic field through the loop changes (increases or decreases). 2) The loop changes in area or angle. 3) The loop moves into or out of a magnetic field. Sample Problem #5 (ex. 25.3, page 824) The switch in the top circuit has been closed for a long time. What happens in the lower loop when the switch is opened? Sample Problem #6 (ex. 25.4, page 825) A loop is moved toward a current carrying wire. As the wire is moving, is there a clockwise current around the loop, a counterclockwise current, or no current? 6
Faraday s Law A change in magnetic flux through a loop creates an induced emf in the loop. This induced emf creates an induced current. Sample Problem #7 (ex. 25.5, page 827) The figure below shows a wire of resistance R sliding on a U-shaped conducting rail. Assume that the conducting rail is an ideal wire. Use Faraday s Law to derive an expression for the current in the wire. Sample Problem #8 (ex. 25.6, page 827) A patient having an MRI scan has neglected to remove a copper bracelet. The bracelet is 6.0 cm in diameter and has a resistance of 0.010 Ω. The magnetic field in the MRI solenoid is directed along the person s body from head to foot; her bracelet is perpendicular to the field. As a scan is taken, the magnetic field in the solenoid decreases from 1.00 T to 0.40 T in 1.2 s. What are the magnitude and direction of the current induced in the bracelet? 7
Don t Copy This James Clerk Maxwell wondered if a changing electric field could create a magnetic field. Maxwell eventually theorized that electric fields can induce magnetic fields, which can induce electric fields. Maxwell showed that these fields are able to sustain themselves, and they take the form of electromagnetic waves. Electromagnetic Waves An EM wave is a transverse wave. EM waves can exist at any frequency, not just the frequencies of visible light. In a vacuum, all EM waves travel with the same speed, a speed that we call the speed of light, for which we use the symbol c. Polarization Unpolarized light consists of waves polarized in all possible directions. A polarizing filter allows light of only a certain polarization to pass through. 8
The Photon Model of EM Waves Many experiments convincingly lead to the surprising result that EM waves, although they are waves, have a particle-like nature. The photon model of EM waves: EM waves consist of discrete, massless units called photons which travel at the speed of light. Each photon has an energy E photon = hf. The superposition of a sufficiently large number of photons has the characteristics of a continuous EM wave. Sample Problem #9 (ex. 25.8, page 835) 550 nm is the approximate average wavelength of visible light. What is the energy of a photon with a wavelength of 550 nm? A 40 W incandescent lightbulb emits about 1 J of visible light energy every second. Estimate the number of visible light photons emitted per second. 9
The EM Spectrum Sample Problem #10 (ex. 25.11, page 839) Ultraviolet radiation with a wavelength of 254 nm is used in germicidal lamps. What is the photon energy in ev for such a lamp? Sample Problem #11 (ex. 25.12, page 840) An x-ray tube used for medical work has an accelerating voltage of 30 kv. An electron is accelerated though this potential difference, hits a metal target, and has its energy converted to an x- ray. What is the maximum energy of an x-ray photon that can be produced in this tube? What is the wavelength of this x-ray? 10