3. Greatest magnitude will be when v and B are perpendicular and will be a minimum when they are parallel; use F = v x B and a = F/m
7. (a) use right hand rule for cross products, crossing v into B which gives direction for a positive charge. (b) Find v from energy of electron, converted to Joules. Then a = F/m. (c) Electron follows circular path. Find radius from centripetal force relationship. To find deflection, draw a diagram of circular arc and find triangle relationship between angle of arc subtended and deflection distance.
12. Electrical and magnetic forces must be equal and opposite, so qE = qvB. Find v from energy of electron (1000 keV).(0.27 mT)
15. Again, electrical and magnetic forces cancel. J = nev, solve for v in terms of B and E.
22 . (a) find v from energy of electron. (2.05 x 107 m/s) (b) use eqn 30-17, solve for B. (0.467 mT) (c) frequency = 1/period, which is speed/distance ( 1.31 x 107 Hz) (d) reciprocal of (c) (7.63 x 10-8 s)
33. (a) Use eqn from problem 31 to find B. (b) If N is number of ions per unit time, current is iqN. Now find rate of deposition in terms of ions and calculate current. (c) Each ion has energy of qV. In elapsed time t, E = NqVt, but Nq = i. All energy will be dissipated as heat.
44. Use eqn 30-25, and 70 degrees as the angle of the cross product. (28.2 N) (b) right hand rule for cross product gives direction for positive charge. (west)
45. Similar to # 44.
52. Magnetic force must push horizontally but can also pull vertically to reduce normal force and friction. At the verge of sliding, net force = 0. Draw free body diagram and write equations for forces in vertical and horizontal directions. Substitute to eliminate variables and get one equation for B in terms of the angle of B with the vertical and given quantities. Find minimum by setting derivative equal to 0 and solving for angle. Substitute angle found into previous expression for B to find its minimum value. (0.10 T)
3. Use eqn 31-8; compare results with value for earth's field.
11. (b) use Biot-Savart law, integrate through semicircle
17. Magnetic field from each segment of wire ( dx) points into page at P. Use Biot-Savart law (eqn 31-5) expressing sin theta and r in terms of x (distance of dx from center of wire and R (distance of P from center of wire). Limits of integration will be L/2 and -L/2.
29. Let d be the distance between the wires. Then, if r is distance from one wire to the point in question, d-r is the distance to the other wire. Set two field expressions equal and solve for r.
32. Field is vector sum of the two fields from each wire. In (a), vertical components cancel and horizontal components equal B cos theta. In (b) horizontal components cancel, but same relationship applies. (4.0 x 10 -4 T)
40. Find value of enclosed current , watch signs.
42, Sketch graph with proper values
53. Plug and chug.
56. Plug and chug.
66. (a) Find area, use eqn 30-30. (b) Use eqn 31-25 (46 cm)