A
a. Find an expression for the induced current I(t) as a function of time.
b. Evaluate I at
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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
- (a) If the emf of a coil rotating in a magnetic field is zero at t = 0, and increases to its first peak at t = 0.100 ms, what is the angular velocity of the coil? (b) At what time will its next maximum occur? (c) What is the period of the output? (d) When is the output first one-fourth at its maximum? (e) When is it next one-fourth at its maximum?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_forwardFigure P30.39 shows a stationary conductor whose shape is similar to the letter e. The radius of its circular portion is a = 50.0 cm. It is placed in a constant magnetic field of 0.500 T directed out of the page. A straight conducting rod, 50.0 cm long, is pivoted about point O and rotates with a constant angular speed of 2.00 rad/s. (a) Determine the induced emf in the loop POQ. Note that the area of the loop is a2/2. (b) If all the conducting material has a resistance per length of 5.00 /m, what is the induced current in the loop POQ at the instant 0.250 s after point P passes point Q? Figure P30.39arrow_forward
- The square armature coil of an alternating current generator has 200 turns and is 20.0 cm on side. When it rotates at 3600 rpm, its peak output voltage is 120 V. (a) Wliat is the frequency' of the output voltage? (b) What is the strength of the magnetic field in which the coil is turning?arrow_forwardFigure P30.41 shows a compact, circular coil with 220 turns and radius 12.0 cm immersed in a uniform magnetic field parallel to the axis of the coil. The rate of change of the field has the constant magnitude 20.0 mT/s. (a) What additional information is necessary to determine whether the coil is carrying clockwise or counterclockwise current? (b) The coil overheats if more than 160 W of power is delivered to it. What resistance would the coil have at this critical point? (c) To run cooler, should it have lower resistance or higher resistance? Figure P30.41arrow_forwardA 50-turn rectangular coil with dimensions 0.15m0.40m rotates in a uniform magnetic field of magnitude 0.75 T at 3600 rev/min. [a) Determine the emf induced in the coil as a function of time, (b) If the coil is connected to a 1000 resistor, what is the power as a function of time required to keep the coil turning at 3600 rpm? (c) Answer part (b) if the coil is connected to a 2000 resistor.arrow_forward
- 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_forwardA constant magnetic field of 0.275 T points through a circular loop of wire with radius 3.50 cm as shown in Figure P32.1. a. What is the magnetic flux through the loop? b. Is a current induced in the loop? Explain. FIGURE P32.1arrow_forwardSuppose a uniform magnetic field is perpendicular to the 81211-in. page of your homework and a rectangular metal loop lies on the page. The loops sides line up with the edges of the page. The magnetic field is changing with time as described by B = 3.75 103 t, where B is in teslas and t is in seconds. a. Is the magnetic field increasing or decreasing? b. Find the magnitude of the emf induced in the loop.arrow_forward
- Review. In Figure P30.42, a uniform magnetic field decreases at a constant rate dB/dt = K, where K is a positive constant. A circular loop of wire of radius a containing a resistance R and a capacitance C is placed with its plane normal to the field. (a) Find the charge Q on the capacitor when it is fully charged. (b) Which plate, upper or lower, is at the higher potential? (c) Discuss the force that causes the separation of charges. Figure P30.42arrow_forwardAn N-turn square coil with side and resistance R is pulled to the right at constant speed v in the presence of a uniform magnetic field B acting perpendicular to the coil as shown in Figure P30.43. At t = 0, the right side of the coil has just departed the right edge of the field. At time t, the left side of the coil enters the region where B = 0. In terms of the quantities N, B, , v, and R, find symbolic expressions for (a) the magnitude of the induced emf in the loop during the time interval from t = 0 to t, (b) the magnitude of the induced current in the coil, (c) the power delivered to the coil, and (d) the force required to remove the coil from the field. (e) What is the direction of the induced current in the loop? (f) What is the direction of the magnetic force on the loop while it is being pulled out of the field? Figure P30.43arrow_forwardA conducting rod of length moves with velocity v parallel to a long wire carrying a steady current I. The axis of the rod is maintained perpendicular to the wire with the near end a distance r away (Fig. P30.44). Show that the magnitude of the emf induced in the rod is E=0Iv2ln(1+lr) Figure P30.44arrow_forward
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