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1 2. An electric dipole consists of 2A. A magnetic dipole consists of a positive charge +Q at one end of a bar magnet with a north pole at one an insulating rod of length d and a end and a south pole at the other. negative charge -Q at the other end. (a) Sketch electric field lines for (a) Sketch magnetic field lines for the dipole shown below. Make clear the dipole shown below. Make clear the direction between the charges. the direction between the poles. These dipoles are now immersed in horizontal fields as shown below: the electric dipole in an electric field and the magnetic dipole in a magnetic field. (e) here (b) Draw the direction of for the (b) Draw the the direction of for the dipole shown on the diagram above. dipole shown on the diagram above. (c) (c) rotation that would be caused by the rotation that would be caused by the torque on the electric dipole? torque on the magnetic dipole? (d) What orientation of the dipole would give stable equilibrium? (d) What orientation of the dipole would give stable equilibrium? (e) Draw, in the space above and to the right of (c), a current loop (show the current direction) with a magnetic dipole moment the same as that of the bar magnet in the diagram for part (b). test continues Page 1

2 3. A long current-carrying cylindrical wire of radius = 1.30 mm has a current i = 9.40 A directed out of the page with a uniform current density. (a) On the cross-sectional diagram, draw magnetic field lines. (b) Using Ampere s Law, derive the formula for the magnetic field inside the wire. Show all steps. (c) Set up the appropriate integral and calculate the total energy stored in the magnetic field in a 1.00 meter length of this wire. (c) There is inductance associated with this wire. Calculate the inductance per unit length of the wire by assuming that the energy stored in the magnetic field is the energy stored in an inductor. test continues Page 2

3 4. Two long straight wires (I 1 = 3.00 A, I 2 = 5.00 A) are parallel to each other and 10.0 cm apart as shown. (a) Label a point S on the diagram where the total magnetic field could be zero. (b) Find the magnetic field at P. Q I I P (c) Draw a vector representing B 1 (due to I 1 at Q) and a vector representing B 2 (due to I 2 at Q) and a vector representing B total (at Q). z 5. An electron is injected into a region of magnetic field with a velocity shown below = (6.00 x 10 7 m/s). The magnetic field = mt is uniform and points into the page in the region indicated. y (a) Sketch, on the diagram to the left, the path of the electron after it enters the magnetic x x x x x x field region. x x x x x (b) What is the magnitude of the magnetic force on the electron? x x x x x x x x x x (c) Which of the following is the formula for the centripetal acceleration? v/r r/v v 2 /r vr vr 2 v 2 r v/r 2 (Circle one.) (d) What is the radius of the path the electron travels in? (e) What electric field, magnitude and direction, must be added to the diagram above in order that the electron travel in a straight line? (f) Does your answer to (e) change if the particle is a proton instead of an electron? yes no (Circle one.) test continues Page 3

4 6. (a) Use the Biot-Savart Law to find the magnetic field at the point P for the two long straight wire segments shown in the diagram below. Make your reasoning clear.... P... (b) Use the Biot-Savart Law to find the magnetic field for the semi-circular wire segment in the diagram in (a). Make all the steps in your reasoning clear. 7. A point charge +Q is located at the center of a hollow, uncharged, conducting sphere with inner radius r 1 and outer radius r 2. (a) How do we know that the electric field inside the metal of the conductor must be zero? +Q (b) How much charge is located where on the hollow conductor? (c) Explain how we prove your answer to the previous part. (d) Derive a formula, showing all steps, for the value of the potential V at the inner surface of the conductor. ecall: E = kq/r 2 for r > r 2 and r < r 1 and V=0 at r -->. test continues Page 4

5 8. (a) The circular wire loop shown below lies in a magnetic field that is into the page and increasing. induced magnetic field? induced current in the loop? (b) In the top view diagram below we see a wire loop and the south pole of a magnet which is being moved towards the loop. side view (i) What is the original direction of the magnetic field on the axis of the loop? v Answer for the side view diagram. N S (ii) induced magnetic field? Answer for the side view diagram. (iii) induced current in the loop on the side view diagram? At which end does the current come out of the page? (iv) induced current in he loop on the front view diagram? front view (looking from the right at the magnet coming towards you) S (c) The rectangular wire loop shown below is moving to the right; at this instant it is partly in the magnetic field which points out of the page. induced magnetic field? induced current in the loop? v (d) The diagram to the right shows a cross section of a wire loop which is rotating clockwise in a magnetic field which points to the right. direction of the induced magnetic field? B direction of the induced current? At which end does the current come out of the page? test continues Page 5

6 (e) A wire loop lies in a horizontal magnetic field and rotates clockwise as shown in the diagram below. B direction of the induced magnetic field? direction of the induced current? 9. In the diagram below, we see a solenoid with a loop A completely inside the solenoid and a loop B completely outside the solenoid. n sol = 2000 turns/m The radius of loop A is 5.00 cm, that of the solenoid solenoid is 8.00 cm, and that of loop B is cm. The loop B current in the solenoid is given by the following function of time: loop A i(t) = 5 amps sin[(120π s -1 ) t] The magnetic field is shown for the instant referred to in part (d) of this question. (a) Write a formula for the voltage induced in Loop A. Substitute as many numbers as possible. (b) Write a formula for the voltage induced in Loop B. 10. (a) Determine the reading on the ammeter in the circuit shown below if the components have the following values: EMF = 20 V, 1 = 3 = 2.00 kω, 2 = 3.00 kω, 4 = 2.26 kω, and the meter has a = 85 Ω. (b) Show (by drawing on the circuit diagram above) how you would connect a voltmeter to the circuit to measure the voltage across 3. test continues Page 6

7 11. In the circuit shown to the right, the values of the components are: = 12.0 V = 500 = 2.00 k L = 200 mh C = 5.00 µf The capacitor is initially uncharged. C (a) At t=0, the switch is closed. Just after the switch is closed, what are the currents I 1 and I 2 through the two resistors 1 and 2? What are the voltages across the four circuit components, V 1 across 1, V L across the inductor, V c across the capacitor, and V 2 across 2? I 1 = I 2 = V c = V 1 = V 2 = V L = L (b) After the switch has been closed for a very long time, what are these quantities? I 1 = I 2 = V c = V 1 = V 2 = V L = (c) What is the time constant associated with the current through the inductor? (d) Sketch (and label) a graph of the potential difference Vc across the capacitor as a function of time. V t (e) On the same axes, and labeling carefully, sketch a graph of the potential drop V 2 across 2 as a function of time. (f) On the same axes, and labeling carefully, sketch a graph of the potential drop V L across L as a function of time. (g) After a long time, the switch is now opened. Just after the switch is opened, what are the values of these quantities? I 1 = I 2 = V c = V 1 = V 2 = V L = E N D Page 7

Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name

Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name Name If you think that no correct answer is provided, give your answer, state your reasoning briefly; append additional sheet of paper if necessary. 1. A particle (q = 5.0 nc, m = 3.0 µg) moves in a region