NAME ______DATE ______CLASS ______
Problem 22A (Induced emf)
ADDITIONAL PRACTICE
1. The Pentagon covers an area of 6.04 x 10^5 m^2, making it one of theworld’s largest office buildings. Suppose a huge loop of wire is placed onthe ground so that it covers the same area as the Pentagon. If the loop ispulled at opposite ends so that its area decreases, an emf will be inducedbecause of the component of Earth’s magnetic field that is perpendicularto the ground. If the field component has a strength of 6.0 x 10^−5 T andthe average induced emf in the loop is 0.80 V, how much time passes beforethe loop’s area is reduced by half?
2. A Japanese-built Ferris wheel has a diameter of 100.0 m and can carryalmost 500 people at a time. Suppose a huge magnet is used to createa field with an average strength of 0.800 T perpendicular to the wheel.The magnet is then pulled away so that the field steadily decreases tozero over time. If the wheel is a single conducting circular loop and theinduced emf is 46.7 V, find the time needed for the magnetic field to
decrease to zero.
3. In 1979, a potential difference of about 32.0 MV was measured in a lab inTennessee. The maximum magnetic fields, obtained for very brief periodsof time, had magnitudes around 1.00 x 10^3 T. Suppose a coil with exactly50 turns of wire and a cross-sectional area of 4.00 x 10^−2 m2 is placed perpendicularto one of these extremely large magnetic fields, which quicklydrops to zero. If the induced emf is 32.0 MV, in how much time does themagnetic field strength decrease from 1.00 x 10^3 T to 0.0 T?
4. The world’s largest retractable roof is on the SkyDome in Toronto,Canada. Its area is 3.2 x 10^4 m2, and it takes 20 min for the roof to fullyretract. If you have a coil with exactly 300 turns of wire that changes itsarea from 0.0 m2 to 3.2 x 10^4 m^2 in 20.0 min, what will be the emf inducedin the coil? Assume that a uniform perpendicular magnetic fieldwith a strength of 4.0 x 10^−2 T passes through the coil.
5. At Massachusetts Institute of Technology, there is a specially shieldedroom in which extremely weak magnetic fields can be measured. As of1994, the smallest field measured had a magnitude of 8.0 x 10^−15 T.Suppose a loop having an unknown number of turns and an area equalto 1.00 m^2 is placed perpendicular to this field and the magnitude of thefield strength is increased tenfold in 3.0 x 10^−2 s. If the emf induced isequal to −1.92 x 10^−11 V, how many turns are in the loop?
6. An electromagnet that has a mass of almost 8.0 x 10^6 kg was built at theCERN particle physics research facility in Switzerland. As part of the detectorin one of the world’s largest particle accelerators, this magnet createsa fairly large magnetic field with a magnitude of 0.50 T. Consider acoil of wire that has 880 equal turns. Suppose this loop is placed perpendicularto the magnetic field, which is gradually decreased to zero in 12 s.