question_answer 50)

  There are two current carrying planar coils made each from identical wires of length L. is circular (radius R) and is square (side a). They are so constructed that they have same frequency of oscillation when they are placed in the same uniform and carry the same current . Find a in terms of R.    

Answer:

                  For circular coil Magnetic moment, For square coil Magnetic moment, Moment of inertia of circular coil about the diameter as axis,  = Moment of inertia of square coil about an axis passing through its centre parallel to breadth . Time period of oscillation of the magnet in magnetic field is given by   and      and  Given,  so   or   On solving, a = 3 R.