BackA closely wound rectangular coil of 80 turns has dimen-sions of 25.0 cm by 40.0 cm. The plane of the coil is rotated from a position where it makes an angle of 37.0° with a magnetic field of 1.70 T to a position perpendicular to the field. The rotation takes 0.0600 s. What is the average emf induced in the coil?
The conducting rod ab shown in Fig. E29.29 makes contact with metal rails ca and db. The apparatus is in a uniform magnetic field of 0.800 T, perpendicular to the plane of the figure. In what direction does the current flow in the rod?
A circular loop in the plane of the paper lies in a 0.65-T uniform magnetic field pointing into the paper. The loop’s diameter changes from 20.0 cm to 8.0 cm in 0.50 s. What is (a) the direction of the induced current, (b) the magnitude of the average induced emf, and (c) the average induced current if the coil resistance is 2.5Ω?
The magnetic field inside a 5.0-cm-diameter solenoid is 2.0 T and decreasing at 4.0 T/s. What is the electric field strength inside the solenoid at a point (a) on the axis and (b) 2.0 cm from the axis?
INT You've decided to make the magnetic projectile launcher shown in FIGURE P30.58 for your science project. An aluminum bar slides along metal rails through a magnetic field B. The switch closes at t = 0 s, while the bar is at rest, and a battery of emf εbat starts a current flowing around the loop. The battery has internal resistance r. The resistances of the rails, which are separated by distance l, and the bar are effectively zero. Show that the bar reaches a terminal speed vterm, and find an expression for vterm.
A rectangular metal loop with 0.050 Ω resistance is placed next to one wire of the RC circuit shown in FIGURE P30.53. The capacitor is charged to 20 V with the polarity shown, then the switch is closed at t = 0 s. What is the current in the loop at t = 5.0 μs? Assume that only the circuit wire next to the loop is close enough to produce a significant magnetic field.
CALC Your camping buddy has an idea for a light to go inside your tent. He happens to have a powerful (and heavy!) horseshoe magnet that he bought at a surplus store. This magnet creates a 0.20 T field between two pole tips 10 cm apart. His idea is to build the hand-cranked generator shown in FIGURE P30.57. He thinks you can make enough current to fully light a 1.0 Ω lightbulb rated at 4.0 W. That's not super bright, but it should be plenty of light for routine activities in the tent. With what frequency will you have to turn the crank for the maximum current to fully light the bulb? Is this feasible?
One way to measure the strength of a magnetic field is with a flip coil. Suppose a 200-turn, 4.0-cm-diameter coil with a resistance of 2.0 Ω is connected to a ballistic galvanometer, a device that measures the total charge passing through. The coil is held perpendicular to the field, then quickly flipped 180° so that the opposite side is facing the magnetic field. Afterward, the galvanometer reads 7.5 μC. What is the field strength? Hint: Use I = dq/dt to relate the net change of flux to the amount of charge that flows through the galvanometer.