PHYS 251 TEST #1 6/9/06 Dr. Holmes NAME
DO ALL EIGHT PROBLEMS. EACH PROBLEM'S WORTH IS MARKED NEXT TO THE PROBLEM. SHOW YOUR WORK FOR PARTIAL CREDIT.
For problems 1 through 4, consider the following situation: point C located at (0 m, +3 m);
qA = +7 mC located at (+6 m, 0 m); qB = -4 mC located at ( -2 m, 0 m).
1) a) What is the magnitude and direction of the force on qB due to the presence of qA ?
magnitude: 3.94 x 10-3 Nt,
direction: right (+x direction, 0o).
b) Is the magnitude of the force on qA due to the presence of qB [smaller than, the same as, or larger than] the magnitude of the force on qB due to the presence of qA ?
same.
c) Is the direction of the force on qA due to the presence of qB [the same as, opposite to, or other than] the direction of the force on qB due to the presence of qA ?
opposite.
2) a) What is the electric field at point C due to qA ONLY ?
magnitude: 1,400 Nt/Coul,
direction: 153.4 degrees.
b) What is the electric field at point C due to qB ONLY?
magnitude: 2,769 Nt/Coul,
direction: 236.3 degrees.
3) What is the total electric field at point C due to BOTH qA and qB?
magnitude: 3,254 Nt/Coul,
direction: 211 degrees.
4) a) If an electron were placed at point C, what would the electric force on the electron be?
magnitude: 5.21 x 10-16 Nt,
direction: 31 degrees.
b) What would be the acceleration of the electron due to this electric force (that is, assume this is the only force on the electron)?
magnitude: 5.74 x 1014 m/s2 ,
direction: 31 degrees.
5) Consider a straight wire of length 20 cm with a uniform charge density of +7 mC/m.
a) What is the electric field 6 cm above the middle of the wire?
magnitude: approx: 2.1x106 Nt/coul; exact: 1.8x106
Nt/Coul.
direction: up, away from the wire.
b) Did you assume that you had a long wire, or did you use the more exact formula to calculate your answer?
c) How far off is the long wire result from the more exact result: [ <1%, 1-10%, 10-50%, >50% ] ?
10-50% .
d) If you move twice as far from the wire (move from the 6 cm above the wire to 12 cm above the wire), does the electric field [get exactly four times smaller, get approximately four times smaller, get exactly 2 times smaller, get approximately 2 times smaller, stay exactly the same, or stay approximately the same] ?
approximately 2 times smaller.
6) A charge of +58 nCoul is placed on a hollow sphere of radius 8 cm.
a) What is the electric field at a point located 15 cm above the center of the sphere (which is outside the sphere)?
magnitude: 23,200 Nt/Coul
direction: up
b) What is the electric field at a point located 15 cm to the left of the surface of the sphere (which is 23 cm to the left of the center of the sphere)?
magnitude: 9,868 Nt/Coul
direction: left (-x, 180o).
c) What is the electric field at a point located 3 cm below the center of the sphere (inside the sphere) ?
magnitude: zero
direction: none
7) Consider a long coaxial cable: at the center of this cable is a wire of radius 4 mm, and around this wire is insulation and then another conductor (cylinder) at a radius of 12 mm. The wire has a charge density of -16 nCoul/m and the cylindrical conductor has a charge density of +16 nC/m.
a) What will the electric field be 10 mm above the axis (6 mm above the surface of the wire, between the cylinder and the wire) ?
magnitude: 28,800 Nt/Coul.,
direction: down, toward from the wire.
b) Will the electric field get [stronger, weaker, or stay the same in magnitude] as you approach the wire (go from 6 mm above the surface of the wire to less than 6 mm above the surface of the wire)?
get stronger.
c) What is the electric field at a distance of 17 mm above the axis (4 mm above the surface of the cylinder)?
magnitude: zero,
direction: (none).
8) Two parallel plates are separated by 6 mm and are each 40 cm by 40 cm in size. An electron is to be released from the bottom plate so as to accelerate to the top plate. When it reaches the top plate a final speed of 1 x 106 m/s is desired. {In the following, if you cannot get an answer to any part, guess an answer for that part, and then use your guess as the basis for the next part. You will be graded on your consistency for each part.}
a) What acceleration does the electron have to have in order to go from zero to 1 x 106 m/s in a distance of 6 x 10-3 m assuming the acceleration is constant?
8.33 x 1013 m/s2 .
b) What force must be on the electron in order to cause this acceleration?
magnitude: 7.58 x 10-17 Nt.
direction: up (+y or 90o).
c) What electric field must be between the plates in order for the electron to have this electric force on it?
magnitude: 474 Nt/Coul
direction: down (-y or 270o).
d) If the two plates have equal (but opposite sign) charge density, what is the magnitude of that charge density for each plate to provide 1/2 the electric field between the plates?
4.19 x 10-9 Coul/m2 = 4.19 nCoul/m2.
e) Which plate should have the positive charge on it [the top or the bottom]?
top.