Please help me answer the following exercises. Show step by step how you got the answer, and please do it on paper so it's easier to understand

Example 19.3 The Mass Spectrometer: Identifying Particles Goal Use the cyclotron equation to identify a particle. Problem A charged particle enters the magnetic field of a mass spectrometer at a speed of 1.79 x 10'i III/S. It subsequently moves in a circular orbit with a radius of 16.0 cm in a uniform magnetic field of magnitude 0.350 T having a direction perpendicular to the particle's velocity. Find the particle's mass-to-charge ratio and identify it based on the table below. Example 19.5 A Current-Carrying Wire in Earth's Magnetic Field Goal Compare the magnetic force on a current-carrying wire with the gravitational force exerted on the wire. Problem A wire carries a current of 22.0 A from west to east. Assume the magnetic field of Earth at this location is horizontal and directed from south to north and it has a magnitude of 0.500 x 104 T. (a) Find the magnitude and direction of the magnetic force on a 36.0-m length of wire. Example 19.2 A Proton Moving in a Magnetic Field Goal Calculate the magnetic force and acceleration when a particle moves at an angle other than 90'\" to the field. Problem A proton moves at 8.00 x 106 m/s along the x-axis. It enters a region in which there is a magnetic field of magnitude 2.50 T. directed at an angle of 60.0\" with the m-axis and lying in the my-plane (g. 19.8). (3] Find the initial magnitude and direction of the magnetic force on the proton. (b) Calculate the proton's initial acceleration. Figure 19.8 _) (ExamQIe 19.2) The magnetic force F on a proton is in the positive z-direction when T" _), and B lie in the xy-plane. The Torque on a Circular Loop in a Magetic Field Goal Calculate a magnetic torque on a loop of current. Problem A circular wire loop of radius 1.00 m is placed in a magnetic eld of magnitude 0.500 T. The normal to the plane of the loop makes an angle of 30.0\" with the magnetic field (g. 19.20a). The current in the loop is 2.00 A in the direction shown. [a] Find the magnetic moment of the loop and the magnitude of the torque at this instant. (b) The same current is carried by the rectangular 2.00-m by 3.00-m coil with three loops shown in gure 19.20b. Find the magnetic moment of the coil and the magnitude of the torque acting on the coil at that instant. Figure 19.20 (Example 19.6) (a) A circular current loop lying in the wy-plane in an external magnetic _> eld B . (b) A rectangular coil lying in the cry-plane in the same field. (c) (Exercise 19.4) 2. f. Example 19.9 The Magnetic Field inside a Solenoid Goal Calculate the magnetic field of a solenoid from given data and the momentum of a charged particle in this field. Problem A certain solenoid consists of 100 turns of wire and has a length of 10.0 cm. (a) Find the magnitude of the magnetic field inside the solenoid when it carries a current of 0.500 A.Example 21.6 Problem Consider a series RLC circuit for which R = 1.50 x 102 0, L = 20.0 mH, AVrms = 20.0 V, and f = 796 s-1. (a) Determine the value of the capacitance for which the rms current is a maximum. (b) Find the maximum rms current in the circuit