A conducting rod is placed on a U-shaped metal conductor containing a 9.0 2 resistor. The rod is moved to the right at a constant speed of 6.2 m/s through a 0.33 T magnetic field as shown. X X X X X X X X X X X X X X 9.0 Ω → v= 6.2 m/s 30 cm X X X X X X X X X X X X X X B = 0.33 T What are the magnitude and direction of the current induced in the rod? 40 cm X X X rod

1.7 x 10-27 kg and a charge 3.0 x 10 m/s in the direction illustrated by a red arrow in the drawing above. The particle enters a region with a uniform magnetic field of magnitude B = 0.1 T (direction is given as a black arrow in the drawing). An angle between velocity and A positively charged particle with a mass m = e = 1.6 x 101 C moves with a speed v = %3D magnetic field vectors is 30 degrees. (a) (E. motion in a plane transverse to B. Show that the radius of this circle is R = Part of the particle's trajectory in this region will be circular 0.16 m. (b) complete revolution around the circle is T = 6.7 x 107 s. Show that the time it takes the proton to execute one (c) Sketch the three-dimensional trajectory of the particle. How far will the particle move in the direction of B in the time T = 6.7 x 10 s?

MOI The strength of the magnetic field B at a distance r from a straight conductor carrying a current I is given by the expression B = 2лr where μo is the permeability of free space with the value 4 x 10-7 NA-2. Two long straight wires are lined up parallel to one another at a separation of 0.17 m. Currents of 4 A and 2 A flow through the wires, both in the same direction. Calculate the absolute value of the magnetic field strength due to the two wires at a point P on the mid-plane between them. Give your answer in micro Tesla (µT, 10-6).

A positively charged particle slides off a frictionless and smooth surface with initial X X X X X X X X speed v, =v, . It then enters into a region with X X X X X x x x X uniform magnetic field pointing into the page. X X X X x x x x X x x x x x X x x x The particle eventually hits the ground with final speed v, air time and range S · The particle slides off the edge again with identical initial speed, but this time without the magnetic field. The particle then hits the ground with final speed v,, air time t, , and range s,. Determine the relationships between v, and v,, t, and t, , as well as s, and s, (3 marks). Please note that no calculation is needed. You were to provide the relationship in the sense that whether one variable is greater than, smaller than, or equals to the other one (>, <, or =). Provide a rough explanation (3 marks).