Physics for Scientists and Engineers: Foundations and Connections
15th Edition
ISBN: 9781305289963
Author: Debora M. Katz
Publisher: Cengage Custom Learning
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Chapter 32.3, Problem 32.3CE
To determine
The direction of
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When the Hemholtz distance condition is satisfied the second derivative of the magnetic field with respect to z vanishes or becomes zero at the center ( point P). Show that both d2Bz/dz2 = 0 and d3Bz/dz3 = 0 at point P.
A circular loop lying on z = 2 m with its center is coinciding with z axis is carrying a current of 20 Amps in −eφ direction . The loop has a radius of a = 3 m, find the magnetic field intensity (H ) at z = 2 m.
A flat square surface with side length 4.50cm is in the xy -plane at z = 0.
Calculate the magnitude of the flux through this surface produced by a magnetic field B =(0.250T)i^+(0.275T)j^+(0.450T)k^.
Express your answer in webers .
Chapter 32 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 32.1 - To calculate the magnetic flux through the...Ch. 32.2 - Prob. 32.2CECh. 32.3 - Prob. 32.3CECh. 32.3 - Prob. 32.4CECh. 32.4 - Prob. 32.5CECh. 32.5 - Prob. 32.6CECh. 32.6 - Prob. 32.7CECh. 32.8 - Prob. 32.8CECh. 32.8 - Prob. 32.9CECh. 32 - A constant magnetic field of 0.275 T points...
Ch. 32 - Prob. 2PQCh. 32 - Prob. 3PQCh. 32 - Prob. 4PQCh. 32 - Prob. 5PQCh. 32 - Figure P32.6 shows three situations involving a...Ch. 32 - A rectangular loop of length L and width W is...Ch. 32 - The magnetic field through a square loop of wire...Ch. 32 - Prob. 9PQCh. 32 - Prob. 10PQCh. 32 - Suppose a uniform magnetic field is perpendicular...Ch. 32 - Prob. 12PQCh. 32 - A square conducting loop with side length a = 1.25...Ch. 32 - A The magnetic field in a region of space is given...Ch. 32 - A The magnetic field in a region of space is given...Ch. 32 - Prob. 16PQCh. 32 - Prob. 17PQCh. 32 - Prob. 18PQCh. 32 - A square loop with side length 5.00 cm is on a...Ch. 32 - A thin copper rod of length L rotates with...Ch. 32 - Figure P32.21 shows a circular conducting loop...Ch. 32 - Prob. 22PQCh. 32 - A square loop with side length L, mass M, and...Ch. 32 - Prob. 24PQCh. 32 - Prob. 25PQCh. 32 - Prob. 26PQCh. 32 - Prob. 27PQCh. 32 - A solenoid of area Asol produces a uniform...Ch. 32 - Two circular conductors are perpendicular to each...Ch. 32 - Two circular conducting loops labeled A and B are...Ch. 32 - Prob. 31PQCh. 32 - Prob. 32PQCh. 32 - Prob. 33PQCh. 32 - Prob. 34PQCh. 32 - Prob. 35PQCh. 32 - Find an expression for the current in the slide...Ch. 32 - The slide generator in Figure 32.14 (page 1020) is...Ch. 32 - Prob. 38PQCh. 32 - A thin conducting bar (60.0 cm long) aligned in...Ch. 32 - A stiff spring with a spring constant of 1200.0...Ch. 32 - A generator spinning at a rate of 1.20 103...Ch. 32 - Suppose you have a simple homemade AC generator...Ch. 32 - Prob. 43PQCh. 32 - Prob. 44PQCh. 32 - Prob. 45PQCh. 32 - Prob. 46PQCh. 32 - A square coil with a side length of 12.0 cm and 34...Ch. 32 - Prob. 48PQCh. 32 - Prob. 49PQCh. 32 - Prob. 50PQCh. 32 - Prob. 51PQCh. 32 - Prob. 52PQCh. 32 - Prob. 53PQCh. 32 - Prob. 54PQCh. 32 - Prob. 55PQCh. 32 - Prob. 56PQCh. 32 - Prob. 57PQCh. 32 - A step-down transformer has 65 turns in its...Ch. 32 - Prob. 59PQCh. 32 - Prob. 60PQCh. 32 - Prob. 61PQCh. 32 - Prob. 62PQCh. 32 - Prob. 63PQCh. 32 - A bar magnet is dropped through a loop of wire as...Ch. 32 - Prob. 65PQCh. 32 - Prob. 66PQCh. 32 - A circular coil with 75 turns and radius 12.0 cm...Ch. 32 - Each of the three situations in Figure P32.68...Ch. 32 - A square loop with sides 1.0 m in length is placed...Ch. 32 - Prob. 70PQCh. 32 - Two frictionless conducting rails separated by l =...Ch. 32 - Imagine a glorious day after youve finished...Ch. 32 - Prob. 73PQCh. 32 - A Figure P32.74 shows an N-turn rectangular coil...Ch. 32 - A rectangular conducting loop with dimensions w =...Ch. 32 - Prob. 76PQCh. 32 - A conducting rod is pulled with constant speed v...Ch. 32 - Prob. 78PQCh. 32 - A conducting single-turn circular loop with a...Ch. 32 - A metal rod of mass M and length L is pivoted...
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- To calculate the magnetic flux through the rectangular loop in Figure 32.2, we used the cross-sectional area A of the solenoid in B = BA (Eq. 32.1). Why didnt we use the area of the rectangular loop?arrow_forwardA toroid has a major radius R and a minor radius r and is tightly wound with N turns of wire on a hollow cardboard torus. Figure P31.6 shows half of this toroid, allowing us to see its cross section. If R r, the magnetic field in the region enclosed by the wire is essentially the same as the magnetic field of a solenoid that has been bent into a large circle of radius R. Modeling the field as the uniform field of a long solenoid, show that the inductance of such a toroid is approximately L=120N2r2R Figure P31.6arrow_forwardTwo frictionless conducting rails separated by l = 55.0 cm are connected through a 2.00- resistor, and the circuit is completed by a bar that is free to slide on the rails (Fig. P32.71). A uniform magnetic field of 5.00 T directed out of the page permeates the region, a. What is the magnitude of the force Fp that must be applied so that the bar moves with a constant speed of 1.25 m/s to the right? b. What is the rate at which energy is dissipated through the 2.00- resistor in the circuit?arrow_forward
- A square loop with side length L, mass M, and resistance R lies in the xy plane. A magnetic field B = B0(y/L) k is present in the region of the space near the loop. Determine the magnitude and direction of the induced current in the loop as the loop starts moving at velocity v = B0(y/L) j.arrow_forwardFigure P32.21 shows a circular conducting loop with a 5.00-cm radius and a total resistance of 1.30 placed within a uniform magnetic field pointing into the page. a. What is the rate at which the magnetic field is changing if a counterclockwise current I = 4.60 102 A is induced in the loop? b. Is the induced current caused by an increase or a decrease in the magnetic field with time?arrow_forwardThe magnetic field strength at an arbitrary point PP on the axis of a circular loop of radius a� carrying current I� is given by Using this equation, find the magnetic field strength at the center of the solenoid’s axis for a solenoid of finite length l and cross-sectional radius a .arrow_forward
- Two straight conducting rails from a right angle as shown in the figure. A conducting bar with the specific resistance of 0.125 per meter is an contact with the rails. The rails have no resistance. The bar starts at the vertex at time t=0 and moves with a constant velocity of 2m/s parallel to the median of the triangle. Conducting rails and the bar are in a uniform magnetic field with the magnitude of B=0.25 T directed into the page. What is the induced current flowing through the bar and its direction at t=2 s?arrow_forwardA molecule with mass m = 255mp (where mp is the mass of a proton) and charge q = −e, moving with a velocity v = 2 × 105 m/s, enters a region of uniform magnetic field B = 0.8 T, as shown in the figure above. The particle strikes the wall at a distance d from the entrance slit. Determine d.arrow_forwardA solenoid is wound with 670 turns, is 50cm long, and is 4cm in diameter as you look down its axis. The current produces a 4mT magnetic field at the center of the solenoid. The magnetic flux, in Tm2, (or Wb) in the solenoid is:arrow_forward
- A very long solenoid of inner radius 2.75 cm creates an oscillating magnetic field B of the form: B = ?maxcos(??). For this solenoid, Bmax is 0.00675 T and ? = 354 rad/s. What is the maximum value Emax of the induced electric field at a perpendicular distance of 1.25 cm from the axis of the solenoid and near the center of the solenoid's length? What is the maximum value of the induced electric field at a perpendicular distance 5.65 cm from the axis of the solenoid and near the center of the solenoid's length?arrow_forwardA long solenoid with 1.00 X 10^3 turns per meter and radius 2.00 cm carries an oscillating current I = 5.00 sin 100 pi t, where I is in amperes and t is in seconds. (a) What is the electric field induced at a radius r = 1.00 cm from the axis of the solenoid? (b) What is the direction of this electric field when the current is increasing counterclockwise in the solenoid?arrow_forwardWe have seen that a long solenoid produces a uniform magnetic field directed along the axis of a cylindrical region. To produce a uniform magnetic field directed parallel to a diameter of a cylindrical region, however, one can use the saddle coils illustrated as shown. The loops are wrapped over a long, somewhat flattened tube.29.46a shows one wrapping of wire around the tube. This wrapping is continued in this manner until the visible side has many long sections of wire carrying current to the left in 29.46a and the back side has many lengths carrying current to the right. The end view of the tube in 29.46b shows these wires and the currents they carry. By wrapping the wires carefully, the distribution of wires can take the shape suggested in the end view such that the overall current distribution is approximately the superposition of two overlapping, circular cylinders of radius R (shown by the dashed lines) with uniformly distributed current, one toward you and one away from you.…arrow_forward
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