Consider a circular loop in a magnetic field. The loop is made of elastic material with spring constant k. It carries a current I and has radius R when unstretched. We immerse it in a magnetic field. The magnitude of the field is B.
(a) Consider the different possible orientations of the loop in the field. We immerse the loop perpendicular to the magnetic field such that the angle ?=90° is subtended between the magnetic field and the plane of the loop. This loop is then pivoted about its center to attain any angle ?. Choose an arc length element and consider the forcing acting on it. Sketch a graph of the magnitude of the force, at above point, as a function of angle ?. Sketch another graph that shows the magnitude of the force in the radial direction as a function of angle ?. (You are free to pick any point on the circumference as long as you indicate it clearly).
?????????????(b) These forces described in part (a) will cause the loop to stretch changing the radius of the loop. Start by considering the change in the distance of two diametrically opposite arc segments for the situation above with ? = 45°. What is the change in radius of this loop?
(c) What is the change in circumference of the loop for ?=90°? (Show us that you know how to setup an integral to calculate circumference from a radius.)