Phys 0175 Spring 2012 - Practice Exam 2 Instructor: Matteo Broccio(1) A region is filled with a uniform magnetic field B = (25 T)y. An electron enters this region with an initial speed v of 624 m/s in the [(4/5)x + (3/5)y] direction. Let the electron be at the origin of your axes. Find the magnetic force acting on the electron, in unit vector notation. A) 4.0·10-13 Nz B) -3.2·10-14 N z C) -2.0·10-15 N z D) 1.6·10-16 N y E) -7.6·10-14 N z(2) Which of the following combinations of units has units of permeability? A) m·kg·s-2·A-2 B) m·kg2·s-1·A-1 C) m2·kg·s·A-1 D) m2·kg2·s·A-1 E) m·kg·s-1·A-1(3) A 3-meter-long conducting cylinder with cross-sectional radius R =2.0 cm has its central axis coinciding with the z axis. The current density J in the cylinder is J(r) = (3.6·103 A/m5)r3z, where r is the radial distance from the z axis. What is the magnitude of the magnetic field observed at position [-(6 mm)x + (4 mm)y]? A) 8.2·10-13 T B) 7.3·10-11 T C) 4.5·10-11 T D) 1.8·10-12 T E) 2.9·10-10 T(4) Consider the circuit below, with Vb= 12 V, R1= 180 Ω, R2= 90 Ω, R3= 120 Ω, R4= 60 Ω. Find the currents i1, i2, and i3 flowing through resistors R1, R2, and R3, respectively. (5) A horizontal wire of mass m and length L carries a current i in the x direction. This wire is hanging from the ceiling (z= constant) through a nonmagnetic spring of force constant k. Let the x-y plane pass through the location where the spring is neither stretched nor compressed. A constant magnetic field B = By is then switched on. Find the new vertical height of the wire at mechanical equilibrium, heq.(6) Using Ampére’s law, derive the expression for the magnetic field inside a solenoid of length L with N turns, carrying a steady current i. (7) A copper wire carries a constant current i in the +z direction (coming out of the paper). A tiny compass, whose small magnetic moment μ does not alter the existing field, is mounted on an nonmagnetic square rail of side length s lying on the x-y plane. The wire is at the center of the rail, and the current is large enough for the compass to feel a torque anywhere on the rail. a) Explain what the compass does at point C and point D in the drawing.b) Find the compass' potential energy at point C.c) Find the compass' potential energy at point D.(8) A rectangular silver loop of length l, width w, and overall resistance R is placed in a constant magnetic field B in the +y direction. Initially (at time t =0), the rectangular loop is all oriented along the x-z plane (see drawing on the left). At later times (t >0), the top half of the loop is folded along the x axis down toward the x-y plane at a constant folding rate ω, while the bottom half is kept in its initial position (see drawing on the right). a) Find the total magnetic flux through the loop as a function of time t (for t >0).b) Find the emf induced at loop ends as a function of time t (for t >0).c) Write the current circulating in the loop as a function of time t (for t
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