NAME. and 2I o. (1) Two long wires carry magnetic fields I o. , where I o


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1 (1) Two long wires carry magnetic fields I o and 2I o, where I o is a constant. The two wires cross at the origin (but without making any electrical connection), and lie in the xy plane. (a) Find the B field at a point, z = h, above the two wires at a point directly above the point where they cross. What is the direction? (b) For the picture above, in what direction should a magnetic field be applied in order to exert a force pointing to the right, on the vertical wire? (i) To the right (v) Into the page (ii) To the left (vi) Out of the page (iii) Upwards (towards top of page) (iv) Downwards (towards bottom of page) (2) For the illustrated circuit, (a) Find the steadystate current in resistor R. (b) Find the steadystate voltage drop across the 2R resistor. 2
2 (3) An emf can be produced in a loop of wire in a uniform magnetic field if (choose the one best answer): a) The field changes in magnitude g) All except b) b) The loop moves horizontally in the field. h) All except c) c) The loop rotates in the field i) All except d). d) The loop is removed from the field region. e) The size of the loop changes. f) All of the above. (4). An object is positioned relative to a converging lens as shown below. The resulting image will be: (Choose the correct answer.) (i) real and inverted (iv) virtual and noninverted (ii) real and noninverted (v) none of the above (iii) virtual and inverted (5) A capacitor has wide, flat plates, and plate separation equal to 0.30 mm. (a) The electric field between plates is equal to 550,000 N/C. What is the voltage difference between the plates? plates? (b) The energy stored in this capacitor is equal to 4.5 mj. What is the area of each the 3
3 (6) A solid sphere is constructed of nonconducting plastic, with radius R. This sphere carries a total charge of Q, distributed uniformly throughout the sphere. (a) What is the charge density on the sphere? (b) Find the electric field at points where r < R, showing your work to obtain credit. (7) A light ray passes from water into air. (The water surface is horizontal, while the dotted line shows the vertical direction.) Of the diagrams, which most clearly resembles the light ray s path? (choose one) (8) A point charge of 2.6 µc is centered at the origin, and completely surrounded by an insulating cube. The point charge is at the center of the cube. Find the flux through one face of the cube. 4
4 (9) Point charges +Q, Q, +2Q and 2Q are arranged at the points of a square as shown. The charges are at ±d on the x axis and ±d on the y axis. (a) Find the electric potential at the point P, relative to infinity. Point P is at position (d, d). (You must show your methods to obtain full credit on this problem.) (b) Find the electric field at the origin. (c) The charge at the top (the one on the positive yaxis) is moved from its illustrated position to the origin. What is the change in total potential energy, if Q = 12 µc, and d = 2.5 cm (values for part c only)? 5
5 (10) The square conducting loop shown has dimensions h by h, and is moving with velocity v to the right. It is about to enter a region of uniform B field, which is indicated by the dotted rectangle. Outside the dotted region, B = 0; inside, the magnitude is B o. (a) If the loop starts to enter the field region at t = 0, find an expression for the magnetic flux vs. time through the loop. (Do this only for times when the loop is partly in the field.) (b) Using your result from (a), find the total emf in the loop during this time. Does it go clockwise or counterclockwise (give a brief explanation)? (c) Determine the current in the loop during this time, if v = 20.0 m/s, h = 3.5 cm, B o = 5.0 T, and the 1turn loop has resistance R = 22 Ω. (d) Describe what happens to the emf during times: (i) when the loop is completely inside the field region; (ii) when it is emerging from the other side. 6
6 (11) A resistor circuit is connected as shown. (a) what is the effective resistance of the four resistors, seen from the battery? (b) Note the two points A and B. If point B is at a potential of 3.0 V, what is the potential at A? (12) Protons of velocity 5x10 6 m/s are moving perpendicular to crossed magnetic and electric fields. (Velocity is perpendicular to both fields.) The protons pass through the region of crossed fields undeflected. If the electric field strength is 15,000 V/m, what is the strength of the magnetic field? 7
7 (13) In this circuit, V B = 15.0 V, C = 15 µf, and R = 30 kω. (Hence, 5R = 150 kω.) The capacitor is uncharged at the start. (a) If the switch is closed at t = 0, at what time will the capacitor voltage drop be 5.0 V? (b) At a later time, if the switch is opened, describe briefly what happens. 8
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