Download PH202 Test 2

PH202 Test 2
• You may not open the textbook nor notebook.
• A letter size information sheet may be used. Only mathematical formula, laws of physics, physical
principles can be written on the sheet. Solutions to homework problems, example problems in the
textbook, or any other problems explained classroom are not allowed in the sheet.
• A calculator may be used. However, mathematics or physics formula programmed in a calculator may
not be used.
• Write down, reasoning, calculation and answer in the blank space after each problem. Use the backside of the sheet if necessary.
• Answers without reasoning, mathematical procedures or other justification will receive no point.
• Don’t forget units in the final answers! Unit is an important part of solutions.
Physical Constants:
electron’s electric charge: e = −1.60 × 10−19 C
electron’s mass: me = 9.11 × 10−31 kg
proton’s mass: mp = 1.67 × 10−27 kg
1
= 8.85 × 10−12 C 2 /(N · m2 ) where k = 8.99 × 109 N · m2 /C 2
permittivity of free space: ǫ0 = 4πk
permeability of free space: µ0 = 4π × 10−7 T · m/A
NAME
SCORE
1
1. A long, straight wire carries a current of I = 2.0A. A charged
particle with −4.0µC is moving at 20 m/s along the wire in direction B shown in Figure 1. The distance between the wire and
charge is 2.0 cm. (Don’t forget to justify your answer including
the direction of vectors.)
(a) [10 pts.] Find the magnitude and direction of the magnetic
field at the position of the charge. The direction should be
specified by a letter (U , D, F , B, L, R) shown in the figure.
(b) [10 pts.] Determine the magnitude and direction of the force
exerted on the charge by the magnetic field. The direction
should be specified by a letter (U , D, F , B, L, R) shown in
the figure.
2
Figure 1
2. An unknown ion X+ is accelerated from rest by an electric potential difference V =2.8 × 104 V and then
enters perpendicularly a uniform magnetic field whose magnitude is B=0.85 T . Its trajectory in the
magnetic field is a circle of radius r= 0.10 m.
(a) [7 pts.] What is the speed of the ion?
(b) [7 pts.] What is the magnitude of the centripetal force exerted on the ion?
(c) [7 pts] Find the mass of the ion. You may not just substitute values into a mathematical expression
for the mass given in a textbook or other places. You must justify your answer from basic
laws/principles of physics and definition of physical quantities.
3
3. A conducting coil of N = 1000 turns is connected to a galvanometer and the total resistance of the
circuit is R = 50.0 Ω. The area of each turn is A = 5.00 × 10−4 m2 . This coil is moved from a region
where the magnetic field is zero into a region where it is uniform and nonzero, the normal to the coil being
kept parallel to the magnetic field. The amount of charge that is induced to flow around the circuit is
measured to be ∆Q = 9.00 × 10−3 C. Use symbols ∆t and B for the duration of the current and magnetic
field, respectively.
(a) [6 pts.] Express the average emf with symbols, R, ∆Q and ∆t [Use Ohm’s law]
(b) [6 pts.] Express the average emf with symbols, N , A, B, and ∆t [Use Faraday’s law]
(c) [6 pts.] Find the magnitude of the magnetic field.
4
Figure 4
4. An aluminum ring is falling and travels over a fixed magnet as
shown in Figures. Answer the following questions. Justify your
answers with words and drawings. (Drawings are required. For
example, you can draws magnetic field lines in the Figures.)
(A) [4 pts.] Determine the direction of induced current when
the ring is above the magnet. Draw an arrow indicating the
current on the ring in Figure (a).
(B) [4 pts.] Determine the direction of force exerted on the ring
by the induced current when the ring is above the magnet.
(Upward or Downward?)
(C) [4 pts.] Determine the direction of induced current when
the ring is below the magnet. Draw an arrow indicating the
current on the ring in Figure (c).
(D) [4 pts.] Determine the direction of force exerted on the ring
by the induced current when the ring is below the magnet.
(Upward or Downward?)
(E) [4 pts.] When the ring is at the center of the magnet (Fig. b),
what is the magnitude of the induced current?
5
5. Figure 5 shows a rectangular 20-turn coil of wire, of dimensions
10 cm by 5.0 cm. It is mounted in the xy plane and hinged along
one long side on the y axis. It carries a current of i = 0.10 A. The
direction of the current is shown in Figure. A uniform magnetic
field of magnitude 0.50 T , is applied at 30◦ from the x axis as
shown in Figure 5.
(a) [7 pts.] Find the magnitude and direction of the torque acting on the coil about the hinge.
(b) [7 pts.] Find the magnitude of the magnetic flux through the
coil.
(c) [7 pts.] The coil rotates 90◦ in 0.2 s. Find emf induced by
the magnetic flux.
6
Figure 5