# PLEASE SHOW ALL WORK AND STEPS A wire loop carries a current i traveling in the…

PLEASE SHOW ALL WORK AND STEPS

A wire loop carries a current i traveling in the clockwise direction The loop is fixed in such a way that it can rotate about the axis (dashed line) shown in the figure. (a) In what direction will the magnetic field need to point for the loop to rotate counter clockwise, w hen viewed from above, about its axis? Explain the reasoning behind your answer. (A) Up (B) Down (C) Left (D) Right (E) Into the Page (F) Out of the Page We are interested in finding the total force exerted on half of the loop. The problem is the angle between the current direction, iL, and the magnetic Held, B, is different everywhere on the loop (see figure), so we cannot easily calculate F = iL times B. (b) To tackle this, let’s divide the loop up into an infinite number of little current segments, idL, each creating a infinitesimal force, dF = idL times B. Set up an integral to calculate the force on half of the loop, dL is a little arc-length. Write an expression for dL in terms of r, the radius of the loop, and d theta, the angle subtended by the arc-length (recall, s r theta). (c) The radius of the loop is 0.012 m, the current in the coil is 0.72 A, and the magnetic field has a strength of 0.36 T. Calculate the magnitude of the force on half of the loop You do not need to provide an assessment of your answer.