RH = I66 CH1= [100 CH2 = 50 PHYS 251 TEST #3 3123/22 Dr. Holmes NAME Key DO ALL EIGHT PROBLEMS. THE WORTH OF EACH PART OF EACH PROBLEM IS MARKED IN THE AREA FOR THE ANSWER. SHOW YOUR WORK FOR PARTIAL CREDIT. IN ALL CASES INVOLVING DIRECTIONS, EXPRESS YOUR ANSWER AS ONE OF THE FOLLOWING: {UP, DOWN, NORTH, EAST, SOUTH, OR WEST}. (DO NOT EXPRESS IT AS INTO THE PAPER OR OUT OF THE PAPER!) USE MKS UNITS IN YOUR ANSWERS @up UNLESS OTHERWISE SPECIFIED. >Z WE down O'N 1) An electron is moving with an initial speed of 7x 105 mls directed down (8) in a location where the magnetic field strength is 0.045 Teslas directed East >. a) What will be the magnetic force on the electron? Magnitude direction? [5] 5.04 x 10'15 Mt [5] North . b) Would the force on a proton moving at the same speed in the same direction in the same magnetic field as the electron be: [(a) the same magnitude and direction, (b) the same magnitude but opposite direction, (c) a smaller magnitude but same direction, or (d) a larger magnitude but opposite direction, or (e) other - please specify] ? (answer a,b,c,d, or else specify) [2] b (same mag, oggosite dir} . 2) A certain mass spectrometer has singly ionized atoms with speed 3.72 x 105 mfs entering a magnetic field of strength 0.345 T. If the ions have a radius of 27 cm in the field, what is the mass of the ions in kilograms? in amu? [6] 4.01 x 10-25 Kg . [2] 24 c) Will Fe-56 ions have a [bigger, the same, or smaller] radius? [2] bigger . 3) A rectangular loop of wire of width (H) 18 cm and length (D 12 cm is placed in a region where the magnetic field is .345 Teslas in strength as shown in the figure below (the North and South poles of the magnet are indicated in the figure by the N and S letters). A current Of 4.2 Amps flows CCW (cou nterclockwise) as viewed from above through the wire. Use the direction convention indicated on the first page (NT, E4, St, We, up, down) a) What will be the magnetic force on the West side of the loop? Magnitude: direction: [2] 0.174 Nt , [2] up . b) What will be the magnetic force on the North side of the loop? Magnitude: direction: [2] 0 , [2] none . c) Will the force on the West side be equal and opposite to that on the East side (yes or no)? [2] Yes . d) Which direction will the TOTAL magnetic FORCE on the rectangular current loop be? (specify direction or answer none if force is zero) [2] 0 . e) Which direction will the total magnetic TORQUE on the rectangular current loop be? (specify direction or answer none if torque is zero) [2] North . pole pole IA 4) DESIGN a DO. electric motor that provides 25 horsepower when it rotates at 2400 rpm. a) Draw a diagram: [4] b) Specify the values of all the parameters: [6] c) What is the average torque generated by your motor? [2] 74.2 Nt*m d) What is the maximum torque generated? [2] 117 Nt*m 5) A circular coil of wire with 2,400 turns each of radius 18 cm carries a current of4.2 Amps directed CW (clockwise) as viewed from above. a) What is the magnetic field at the center of the loop? Magnitude: direction: [5] 3.51 x 10'2 T , [5] down . b) If the same current is maintained, but the radius of the circular loop is made larger with the number of turns decreased (so the amount of wire remains the same), will the field at the center of the coil be [bigger, remain the same, or be smaller]? [2] smaller . 6) A solenoid has a length of 36 cm, a radius of 4cm, and 2,400 windings wound around it. A current of 4.2 amps flows through the solenoid. a) What is the magnitude of the magnetic field at the center of the solenoid? z .0352 [4] = .0343 T . b) Is this an "exac " or "approximate" calculation? [2] . C) Is the "approximate" value higher, the same, or lower than the "exact" value? [2] higher . d) In this case, by what percent does the "approximate" value differ from the "exact" value? [2] 2.4% . 7) A moving electron at a certain instant is located 7 mm West of a long straight wire that carries a current of 4.2 amps due North. a) If the electron is moving East (towards the wire) with a speed of4x105 mls, what is the magnetic force on the electron at this instant? Magnitude: direction: [4] 7.68 x 10'13 Mt , [4] North b) What is the acceleration that the electron will undergo at this instant if this is the only force on the electron? Magnitude: direction: [2] 8.44 x 1012 mi's2 , [2] North . c) Will this acceleration speed up the electron, slow it down, turn it, or not affect the it's motion since the acceleration is zero? [2] turn it . d) If the electron were moving South (anti-parallel to the current) instead of East, would the magnitude of the magnetic force on the electron be greater, be the same, or be less? [2] same . e) lfthe electron were moving North (parallel to the current) instead, what would the direction of the magnetic force on the electron now be (if zero force, answer NIA). [2] West . 8) Consider the two currents in the figure below. a) Is the net magnetic force between the currents attractive, zero, or repulsive? [2] repulsive . b) What is the magnitude of the net magnetic force on the rectangular current? [6] 8.4 x 10"5 Mt . o) Is the magnitude of the net magnetic force on the straight current bigger, the same, or smaller than the magnitude of the net magnetic force on the rectangular current? [2] same Iwire = 4.2 Amps; Irectangular = 3Amps, w = 20 cm; near distance to straight wire = 4 cm; distance from far side to straight wire = 12 cm . 20 cm ;qp > lrectangular > 120m