The loop of wire shown in Fig. P27.71 forms a right triangle and carries a current I = 5...

The loop of wire shown in Fig. P27.71 forms a right triangle and carries a current I = 5.00 A in the direction shown. The loop is in a uniform magnetic field that has magnitude B = 3.00 T and the same direction as the current in side PQ of the loop. (a) Find the force exerted by the magnetic field on each side of the triangle. If the force is not zero, specify its direction. (b) What is the net force on the loop? (c) The loop is pivoted about an axis that lies along side PR. Use the forces calculated in part (a) to calculate the torque on each side of the loop (see Problem 27.70). (d) What is the magnitude of the net torque on the loop? Calculate the net torque from the torques calculated in part (c) and also from Eq. (27.28). Do these two results agree? (e) Is the net torque directed to rotate point Q into the plane of the figure or out of the plane of the figure?

27.70 .. CALC A uniform bar of length L carries a current I in the direction from point a to point b (Fig. P27.70). The bar is in a uniform magnetic field that is directed into the page. Consider the torque about an axis perpendicular to the bar at point a that is due to the force that the magnetic field exerts on the bar. (a) Suppose that an infinitesimal section of the bar has length dx and is located a distance x from point a. Calculate the torque about point a due to the magnetic force on this infinitesimal section. (b) Use to calculate the total torque t on the bar. (c) Show that is the same as though all of the magnetic force acted at the midpoint of the bar.