3. To monitor the breathing of a hospital patient, a thin belt (a 200-turn coil) is placed around the patient's chest. Suppose that the belt has a radius of 20 cm and when the patient inhales, the belt expands to a radius of 20.5 cm. The magnitude of the Earth's magnetic field is 50.0 T and makes an angle of 50° with the normal to the coil. Assuming that a patient takes 1.80 s to inhale, find the average induced emf in the coil during this time. What is the induced emf when the person exhales over the same time interval. ELECTROMAGNETIC PHENOMENA 1. Electromagnetic induction Magnetic flux is a measurement of the total magnetic field B which passes through a given area. It is a useful tool for helping describe the effects of the magnetic force on something occupying a given area. If the magnetic field is constant, the magnetic flux passing through a surface of area A is Normal to A Фв 3D В - А-соs® The SI unit of magnetic flux is the Weber (Wb). Faraday law When a current conducting wire or coil is moved through a magnetic field a voltage (EMF) is generated which depends on the magnetic flux through the area of the coil. This is an example of the phenomenon of electromagnetic induction; the current that flows in this situation is known as an induced current. B cos e Faraday's Law relates the average induced EMF in terms of the time rate of change of the total magnetic flux through a current O = BA cos 0 = B,A conductor or coil. ДФв Δt Finally, if a coil has N turns, an emf will be produced that is N times greater than for a single coil, so that emf is directly proportional to N . The magnetic field strength (magnitude) produced by a long straight current-carrying wire is found by experiment to be B = 0, where I is the current, r is the shortest distance to the wire, and the constant µo = 4xx10¯7 T · m/A is the permeability of free space. Magnetic field produced by a current-carrying circular loop. There is a simple formula for the magnetic field strength at the center of a circular loop. It is B = , where R is the radius of the loop. One way to get a larger field is to have N loops; then, the field is B = NH. 2. Electromagnetic field At every instant the ratio of the magnitude of the electric field to the magnitude of the magnetic field in an electromagnetic wave equals the speed of light. Emax _ E Bmax %3D 3. Electromagnetic waves The magnitudes electric field strength E and magnetic field strength B in electromagnetic wave vary with x and t according to the expressions E(x,t) = E,sin(kx – wt) B(x, t) = B,sin(kx – wt) Here k = and w == with A the wavelength and T the period of the wave (T=1/fwherefis the frequency of oscillation of the wave). The speed of the wave is given by v = c = w /k. There are many types of waves, such as water waves and even earthquakes. Among the many shared attributes of waves are propagation speed v, frequency f, and wavelength A. These are always related by the expression: v = af Electromagnetic waves, like visible light, infrared, ultraviolet, X-rays, and gamma rays don't need a medium in which to propagate; they can travel through a vacuum. Speed of electromagnetic wave in vacuum VHOE0 Taking the permittivity of free space ɛ, = 8.85 · 10-12 F/m and permeability of free space uo = 4nx10-7 T-m/A, c = 3· 10° m/sec. Table Electromagnetic Waves Type of EM Life sciences Production Applications Issues aspect wave Communications Remote controls Accelerating charges & thermal Communications Ovens Deep heating Radar Requires controls for band use Accelerating charges MRI Radio & TV Microwaves Cell phone use agitation Thermal agitations & electronic Thermal imaging transitions Absorbed by atmosphere Photosynthesis Human vision Greenhouse effect Intrared Heating Thermal agitations & electronic transitions All pervasive Visible light Sterilization Cancer control Thermal agitations & electronic transitions Inner elecronic transitions and fast collisions Ozone depletion Cancer causing Ultraviolet Vitamin D production Medical diagnosis Cancer therapy Medical Security Cancer causing Х-лаys Medical diagnosis Cancer therapy Nuclear medicineSecurity Cancer causing Radiation damage Gamma rays Nuclear decay 4. Energy in electromagnetic wave Electromagnetic waves can bring energy into a system by virtue of their electric and magnetic fields. These fields can exert forces and move charges in the system and, thus, do work on them. Once electromagnetic wave has created, the fields carry energy away from a source. Intensity I of electromagnetic wave is energy per area A per time t or power P per area. Intensity is Energy measured in W/m?: I = The energy carried and the intensity I of an electromagnetic wave is proportional to E and B. In fact, for a continuous sinusoidal electromagnetic wave, the average intensity I is given by ce,E , where c is the speed of light, ɛo is the permittivity of free space, and Eo is the maximum electric field strength. The average intensity of an electromagnetic wave I can also be expressed in terms of the magnetic field strength I = i, where Bo is the maximum magnetic field strength. 2Ho 5. Radiation pressure is the pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. The radiation pressure P exerted on the perfectly absorbing surface is: P = - 6. The electromagnetic wave intensity at distance r from the source I = 4r here p is power.