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(Solved): A thin coil (primary) with radius a=5.0cm (cross-sectional area, A1=79cm2 ) and N1=200 tu ...
A thin coil (primary) with radius (cross-sectional area, ) and turns is situated (concentric and co-planar) around a thin coil (secondary) with cross-sectional area, and turns. The time dependence of the current in the primary coil is a) Calculate the magnetic field at the center of the primary coil at b) Calculate the magnetic flux through the secondary coil at assuming that the magnetic field is approximately uniform within the secondary coil. c) Write the expression for the magnitude of the emf in the secondary coil as a function of time. e) Find the mutual inductance of this coil pair.
Expert Answer
a) To calculate the magnetic field at the center of the primary coil at t=0, we can use the formula: where is the permeability of free space ( ), N1 is the number of turns in the primary coil, i1 is the current in the primary coil, and a is the radius of the primary coil.At t=0, i1 = 10 A. Substituting the given values, we get: Therefore, the magnetic field at the center of the primary coil at t=0 is 0.0503 T.