.A rectangular coil consists of N = 100 closely wrapped m turns and has dimensions a = 0.400 m and b = 0.300 m. The coil is hinged along the y axis, and its plane makes an angle 6 = 30.0 with the xaxis (Fig. P2951). (a) What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = 0.800 T directed in the positive x direction when the current is I = 1.20 A in the direction shown? (b) What is the expected direction of rotation of the coil? Figure P29.51 71. Figure P2971 shows a schematic representation of an apparatus that can be used to measure magnetic fields. A rectangular coil of wire contains N turns and has a width w. The coil is attached to one arm of a balance and is suspended between the poles of a magnet. The magnetic eld is uniform and perpendicular to the plane of the coil. The system is rst balanced when the current in the coil is zero. When the switch is closed and the coil carries a current I, a mass m must be added to the right side to balance the system. (a) Find an expression for the magnitude of the magnetic field. (b) Why is the result independent of the vertical dimen- sions of the coil? (c) Suppose the coil has 50 turns and a width of 5.00 cm. When the switch is closed, the coil carries a current of 0.300 A, and a mass of 20.0 g must be added to the right side to balance the system. What is the magnitude of the magnetic eld? I Figure P2931 73. A uniform magnetic field of magnitude 0.150 T is directed along the positive x axis. A positron moving at a speed of 5.00 X 105 m/s enters the field along a direc- tion that makes an angle of 0 = 85.0' with the x axis (Fig. P29.73). The motion of the particle is expected to be a helix as described in Section 29.2. Calculate (a) the pitch p and (b) the radius r of the trajectory as defined in Figure P29.73. 2- B X Figure P29.7378. Protons having a kinetic energy of 5.00 MeV (1 eV = 1.60 X 10 " J) are moving in the positive x direction and enter a magnetic field B = 0.050 0k T directed out of the plane of the page and extending from x = 0 to x = 1.00 m as shown in Figure P29.78. (a) Ignoring relativistic effects, find the angle a between the initial velocity vector of the proton beam and the velocity vec- tor after the beam emerges from the field. (b) Calcu- late the y component of the protons' momenta as they leave the magnetic field.