Magnetic Fields VI Name: ____________________ # of problems you seriously attempted = _____ Magnetic Fields VI Magnetic Fields VI 2. The figure shows two circular regions with radii R1 = 20 cm and R2 = 30 cm. Everywhere within R1 there is a uniform magnetic field B1 = 50 mT out of the page, and everywhere within R2 there is a uniform mangetic field B2 = 75 mT into the page. Both fields are decreasing at a rate of 8.50 mT/s (i.e., this number equals –dB/dt). Calculate the integral E   E  dl (which equals a voltage) for each of the three given paths. Path 3 Path 2 R1 × R2 Path 1 Magnetic Fields VI 3. In the figure, the magnetic field in the circular region increases with time according to B = (2.00t3 - 4.00t2 + 0.800) Teslas, with r = 2R = 5.00 cm. Calculate the magnitude and direction of the force exerted on an electron located at point P at t = 2.00s. P × × F × × × × × × × × × × r × R Bin Magnetic Fields VI 4. An electric field of 300 V/m is confined to a circular area 10.0 cm in diamter and directed outward perpendicular to the plane of the fiugre. If the electric field is increasing at a rate of 20.0 V/m·s, what are the direction and magnitude of the magnetic field at point P, 15.0 cm from the center of the circle? Magnetic Fields VI HOMEWORK 1. Wolfson, Volume II, 2nd Edition, 27.30 2. Wolfson, Volume II, 2nd Edition, 27.49 (1 fN = 1 femtonewton = 10-15 N) Magnetic Fields VI 3. MRI (magnetic resonance imaging) is very safe because it doesn’t deliver ionizing radiation like x-rays do. One possible concern with MRIs is turning the magnetic field on or off too quickly. Bodily fluids are conductors, and a changing magnetic field could cause electric currents to flow through the patient. Suppose a typical patient has a maximum cross-sectional area of 0.060 m2. What is the smallest time interval in which a 5.0T magnetic field can be turned on or off if the induced emf around the patient’s body must be kept to less than 0.10 V? If the person’s cross-section is approximated as a circle, what maximum electric field around the body’s perimeter corresponds to this emf? 4. Wolfson, Volume II, 2nd Edition, 29.13 Magnetic Fields VI 5. Wolfson, Volume II, 2nd Edition, 29.35 Magnetic Fields VI