An instrument based on induced emf has been used to measure projectile speeds up to 6 km/s. A small magnet is imbedded in the projectile as shown in Figure P23.2. The projectile passes through two coils separated by a distance d. As the projectile passes through each coil, a pulse of emf is induced in the coil. The time interval between pulses can be measured accurately with an oscilloscope, and thus the speed can be determined. (a) Sketch a graph of ΔV versus t for the arrangement shown. Consider a current that flows counterclockwise as viewed from the starting point of the projectile as positive. On your graph, indicate which pulse is from coil 1 and which is from coil 2. (b) If the pulse separation is 2.40 ms and d = 1.50 m, what is the projectile speed?
Figure P23.2
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Principles of Physics: A Calculus-Based Text
- A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in Figure P23.7. (a) Determine the magnetic flux through the loop due to the current I. (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the emf that is induced in the loop if b = 10.0 A/s, h = 1.00 cm, w = 10.0 cm, and L = 1.00 m. (c) What is the direction of the induced current in the rectangle? Figure P23.7arrow_forwardFigure P23.58 is a graph of the induced emf versus time for a coil of N turns rotating with angular speed ω in a uniform magnetic field directed perpendicular to the coil’s axis of rotation. What If? Copy this sketch (on a larger scale) and on the same set of axes show the graph of emf versus t (a) if the number of turns in the coil is doubled, (b) if instead the angular speed is doubled, and (c) if the angular speed is doubled while the number of turns in the coil is halved. Figure P23.58arrow_forwardA bar magnet is held in a vertical orientation above a loop of wire that lies in the horizontal plane as shown in Figure OQ23.13. The south end of the magnet is toward the loop. After the magnet is dropped, what is true of the induced current in the loop as viewed from above? (a) It is clockwise as the magnet falls toward the loop. (b) It is counterclockwise as the magnet falls toward the loop. (c) It is clockwise after the magnet has moved through the loop and moves away from it. (d) It is always clockwise. (e) It is first counterclockwise as the magnet approaches the loop and then clockwise after it has passed through the loop.arrow_forward
- A bar of mass m and resistance R slides without friction in a horizontal plane, moving on parallel rails as shown in Figure P30.49. The rails are separated by a distance d. A battery that maintains a constant emf E is connected between the rails, and a constant magnetic field B is directed perpendicularly out of the page. Assuming the bar starts from rest attime t = 0, show that at time t it moves with a speed.arrow_forwardA constant magnetic field passes through a single rectangular loop whose dimensions are 0.26 m x 0.79 m. The magnetic field has a magnitude of 3.1 T and is inclined at an angle of 78 degrees with respect to the normal to the plane of the loop. (a) If the magnetic field decreases to zero in a time of 0.62 s, what is the magnitude of the average emf induced in the loop? (b) If the magnetic field remains constant at its initial value of 3.1 T, what is the magnitude of the rate Delta A/ Delta t at which the area should change so that the average emf has the same magnitude?arrow_forwardA Figure P32.74 shows an N-turn rectangular coil of length a and width b entering a region of uniform magnetic field of magnitude Bout directed out of the page. The velocity of the coil is constant and is upward in the figure. The total resistance of the coil is R. What are the magnitude and direction of the magnetic force on the coil a. when only a portion of the coil has entered the region with the field, b. when the coil is completely embedded in the field, and c. as the coil begins to exit the region with the field?arrow_forward
- A square coil with a side length of 12.0 cm and 34 turns is positioned in a region with a horizontally directed, spatially uniform magnetic field of 82.0 mT and set to rotate about a vertical axis with an angular speed of 1.20 102 rev/min. a. What is the maximum emf induced in the spinning coil by this field? b. What is the angle between the plane of the coil and the direction of the field when the maximum induced emf occurs?arrow_forwardThe magnetic field through a square loop of wire with sides of length 3.00 cm changes with time as shown in Figure P32.8, where the sign indicates the direction of the field relative to the axis of the loop. Plot the emf induced in the loop versus time. FIGURE P32.8arrow_forwardA rectangular conducting loop with dimensions w = 32.0 cm and h = 78.0 cm is placed a distance a = 5.00 cm from a long, straight wire carrying current I = 7.00 A in the downward direction (Fig. P32.75). a. What is the magnitude of the magnetic flux through the loop? b. If the current in the wire is increased linearly from 7.00 A to 15.0 A in 0.230 s, what is the magnitude of the induced emf in the loop? c. What is the direction of the current that is induced in the loop during this time interval?arrow_forward
- A long, straight wire carries a current given by I = Imax sin (t + ). The wire lies in the plane of a rectangular coil of N turns of wire as shown in Figure P30.45. The quantities Imax, , and are all constants. Assume Imax = 50.0 A, = 200 s1, N = 100, h = = 5.00 cm, and L = 20.0 cm. Determine the emf induced in the coil by the magnetic field created by the current in the straight wire. Figure P30.45arrow_forwardA long solenoid, with its axis along the x axis, consists of 200 turns per meter of wire that carries a steady current of 15.0 A. A coil is formed by wrapping 30 turns of thin wire around a circular frame that has a radius of 8.00 cm. The coil is placed inside the solenoid and mounted on an axis that is a diameter of the coil and coincides with the y axis. The coil is then rotated with an angular speed of 4.00 rad/s. The plane of the coil is in the yz plane at t = 0. Determine the emf generated in the coil as a function of time.arrow_forwardReview. Figure P31.31 shows a bar of mass m that can slide without friction on a pair of rails separated by a distance and located on an inclined plane that makes an angle with respect to the ground. The resistance of the resistor is R. and a uniform magnetic field of magnitude H is directed downward, perpendicular to the ground, over the entire region through which the bar moves. With what constant speed v does the bar slide along the rails?arrow_forward
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