PHYS 251 TEST #3 6/23/06 Dr. Holmes NAME

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!)

1) A proton is moving with an initial speed of 4 x 105 m/s directed up in a location where the magnetic field strength is .033 Teslas directed East.

a) What will be the magnetic force on the proton?

magnitude: 2.11 x 10-15 Nt.

direction: North.

b) Would the force on an electon moving at the same speed in the same direction in the same magnetic field as the proton 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)

b (same magnitude but opposite direction).

2) A cyclotron consists of a pair of "dees" with radius 22 cm placed in a constant and uniform magnetic field of strength 1.7 Teslas. An accelerating voltage of 1,200 volts is employed. If the cyclotron is used to accelerate nitrogen ions (q=+e, m=14 amu):

a) What will be the maximum speed of the nitrogen ions from this cyclotron?

2.56 x 106 m/s.

b) What will the energy of the nitrogen ions be when they emerge with this maximum speed?

In Joues: 7.66 x 10-14 J in electron volts (eV): 4.78 x 105 eV.

c) What should the frequency of the alternating voltage be?

1.85 x 106 Hz.

d) Will the maximum energy of the nitrogen ions be increased by (answer Yes or No):

(1) increasing the radius of the "dees"? Yes

(2) increasing the accelerating voltage? No

(3) increasing the magnetic field strength? Yes.

3) A rectangular loop of wire of width («) 6 cm and length 5 cm (b ) is placed in a region where the magnetic field is .033 Teslas in strength as shown in the figure to the right (the North and South poles of the magnet are indicated in the figure by the N and S letters). A current of 1.7 Amps flows clockwise (as viewed from above) through the wire. Use the direction convention indicated on the first page (N­ , E® , S¯ , W¬ , up¤ , downÄ )

a) What will be the magnetic force (magnitude and direction) on the North side of the loop?

magnitude: zero

direction: none.

b) What will be the magnetic force (magnitude and direction) on the West side of the loop?

magnitude: 2.81 x 10-3 Nt

direction:  down.

c) Will the force on the West side be equal and opposite to that on the East side (yes or no)?

Yes.

d) Which direction will the TOTAL magnetic FORCE on the rectangular current loop be? (specify direction or answer none if force is zero)

none.

e) Which direction will the total magnetic TORQUE on the rectangular current loop be? (specify direction or answer none if torque is zero)

South.

4) DESIGN a D.C. electric motor that provides 4 horsepower when it rotates at 6,000 rpm.

a) Draw a diagram:

b) Specify the values of all the parameters:

c) What is the average torque generated by your motor?

4.75 Nt-m.

d) What is the maximum torque generated?

7.46 Nt-m.

5) A circular ciol of wire of 250 turns each of radius 6 cm carries a current of 2.1 Amps directed counterclockwise as viewed from above.

a) What is the magnetic field (magnitude and direction) at the center of the loop?

magnitude: 5.5 x 10-3 T = 55 Gauss

direction: up.

b) If the same current is maintained in the same length of wire, but the radius of the circular loop is made smaller and so the number of turns is correspondingly bigger, will the field at the center of the loop be bigger, remain the same, or be smaller?

bigger.

6) A solenoid has a length of 27 cm, a radius of 2 cm, and 2,100 windings wound around it. A current of 2.1 amps flows through the solenoid.

a) What is the magnitude of the magnetic field at the center of the solenoid?

approximate: .0205 T = 205 Gauss.

exact: .0203 T = 203 Gauss.

b) Is this an "exact" or "approximate" calculation?

c) Is the "approximate" value higher, the same, or lower than the "exact" value?

higher.

d) In this case, by what percent does the "approximate" value differ from the "exact" value ?

1.1%.

7) A moving electron at a certain instant is located 5 mm North of a long straight wire that carries a current of 2.1 amps due East.

a) If the electron is moving West (anti-parallel with the wire) with a speed of 3 x 105 m/s, what is the magnitude and direction of the magnetic force on the electron at this instant?

magnitude: 4.03 x 10-18 Nt

direction: South.

b) What is the magnitude and direction of the acceleration the electron will undergo at this instant if this is the only force on the electron?

magnitude: 4.43 x 1012 m/s2 .

direction: South.

c) Will this acceleration speed up the electron, slow it down, turn the electron, or not affect the electron's motion since the acceleration is zero?

turn.

d) If the electron were moving South (toward the current) instead of West, would the magnitude of the magnetic force on the electron increase, stay the same, or decrease?

same.

e) If the electron were moving South (toward the current) instead of West, what would the direction of the magnetic force on the electron now be (if zero force, answer N/A).

East.

8) Consider the two currents in the figure to the right.

a) Is the net magnetic force between the currents attractive, zero, or repulsive?

attractive.

b) What is the magnitude of the net magnetic force on the rectangular current?

6.0 x 10-6 Nt .

c) 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?

same.