The schematic below depicts a rectangular wire loop with side lengths L and 2L that has an a constant electric current of unknown magnitude I running through it clockwise as indicated by the orange arrows. This wire loop is in a location with a uniform and constant external magnetic field B pointing in the z- direction. The wire loop has a total mass m and is held in a horizontal position (parallel to the z-x-plane) by a rope that is attached to one of the short sides of the loop (labeled side 1 in the schematic). This rope. exerts an upward tension force of unknown magnitude Frope. top front view Frope = Fropeŷ B = B₂ I top side view Frope 2L L 2L (i) [4pts] Find the magnetic force FB on the entire wire loop, by adding up the magnetic forces on each of the four sides: = FB,1 FB,2 = FB,3 = FB,A = ⇒ FB = (ii) [3pts] Use your knowledge of the total force F net on the wire loop to find the unknown tension force Frope. (iii) [10pts] Considering the torque Trope = × Frope imparted on the wire loop (with respect to its center of mass) by the rope and the magnetic torque 7B = μ× B, find an expression for the unknown electric current I using only the given parameters or natural constants. At time t = 0, an electron is moving on the negative z-axis with unknown speed vo in the positive z-direction and may be considered force-free at this time (the gravitational pull in the negative y-direction shall be neglected in this problem). When the particle reaches the origin, it experiences a uniform and con- stant electric field Ē = E and a uniform and constant magnetic field B = Bŷ in the half- space z 0, as indicated in the schematic. = voz (i) [5pts] Suppose you observe that the electron stays on its straight trajectory along the z-axis after it enters the electromagnetic fields. - Determine the unknown original speed vo. - Does the electron speed remain constant at z>0? (Yes / No) - Would the trajectory of a positively charged particle with the same initial velocity be different? (Yes/No) (ii) [4pts] Consider the scenario in which only the E-field is present at z> 0. What can you say about the magnitude and direction of the electron velocity a long time after the electron enters the E-field? For t∞, v: ϋ: = X voz 1 Z (iii) [4pts] Now consider the scenario in which only the B-field is present at z > 0. What can you say about the magnitude and direction of the electron velocity a long time after the electron enters the B-field? For t∞, v: = voz ϋ: