Problem 10: A magnetic needle with magnetic moment μ-0.065 Am2 is placed in a uniform magnetic field B0.65 T as shown in the figure. The angle between the direction of the magnetic moment and the direction of the magnetic field is θ 250 Randomized Variables μ= 0.065 Arn B- 0.65T θ 250 Δ Part (a) Express the potential energy U in terms oft, B, θ. | cos(p) sin(p) | cos(α) sin(a) cos(0) sin(0) ( HOMI 4 5 6 BACKSPACE CLEAR Submit Hint I give up! Hints: 1% deduction per hint. Hints remaining: 1 Feedback: 1% deduction per feedback. Part (b) Calculate the numerical value of U in J. Part (c) If θ can be changed, which value has the minimum potential energy? Part (d) If θ can be changed, which value has the maximum potential energy in degrees? Δ Part (e) Ignore the mass of the needle, express the work needed to change the angle from θ to α in terms oftı, B, θ, α Part (f) If α-1500, calculate the numerical value of the work in J.

Problem 10: A magnetic needle with magnetic moment μ-0.065 Am2 is placed in a uniform magnetic field B0.65 T as shown in the figure. The angle between the direction of the magnetic moment and the direction of the magnetic field is θ 250 Randomized Variables μ= 0.065 Arn B- 0.65T θ 250 Δ Part (a) Express the potential energy U in terms oft, B, θ. | cos(p) sin(p) | cos(α) sin(a) cos(0) sin(0) ( HOMI 4 5 6 BACKSPACE CLEAR Submit Hint I give up! Hints: 1% deduction per hint. Hints remaining: 1 Feedback: 1% deduction per feedback. Part (b) Calculate the numerical value of U in J. Part (c) If θ can be changed, which value has the minimum potential energy? Part (d) If θ can be changed, which value has the maximum potential energy in degrees? Δ Part (e) Ignore the mass of the needle, express the work needed to change the angle from θ to α in terms oftı, B, θ, α Part (f) If α-1500, calculate the numerical value of the work in J.

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Magnetic Fields

Section: Chapter Questions

Problem 34P: A rectangular loop of wire has dimensions 0.500 m by 0.300 m. The loop is pivoted at the x axis and...

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A magnetic field directed into the page changes with time according to B = 0.030 0t2 + 1.40, where B is in teslas and t is in seconds. The field has a circular cross section of radius R = 2.50 cm (see Fig. P23.28). When t = 3.00 s and r2 = 0.020 0 m, what are (a) the magnitude and (b) the direction of the electric field at point P2?
Within the green dashed circle show in Figure P30.21, the magnetic field changes with time according to the expression B = 2.00t3 4.00t2 + 0.800, where B is in teslas, t is in seconds, and R = 2.50 cm. When t = 2.00 s, calculate (a) the magnitude and (b) the direction of the force exerted on an electron located at point P, which is at a distance r = 5.00 cm from the center of the circular field region. (c) At what instant is this force equal to zero? Figure P30.21
Two 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?
A conducting single-turn circular loop with a total resistance of 5.00 is placed in a time-varying magnetic field that produces a magnetic flux through the loop given by B = a + bt2 ct3, where a = 4.00 Wb, b = 11.0 Wb/s2, and c = 6.00 Wb/s3. B is in webers, and t is in seconds. What is the maximum current induced in the loop during the time interval t = 0 to t = 3.50 s?
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A rectangular loop of wire has dimensions 0.500 m by 0.300 m. The loop is pivoted at the x axis and lies in the xy plane as shown in Figure P28.34. A uniform magnetic field of magnitude 1.50 T is directed at an angle of 40.0 with respect to the y axis with field lines parallel to the yz plane. The loop carries a current of 0.900 A in the direction shown. (Ignore gravitation.) We wish to evaluate the torque on the current loop. (a) What is the direction of the magnetic force exerted on wire segment ab? (b) What is the direction of the torque associated with this force about an axis through the origin? (c) What is the direction of the magnetic force exerted on segment cd? (d) What is the direction of the torque associated with this force about an axis through the origin? (e) Can the forces examined in parts (a) and (c) combine to cause the Loop to rotate around the x axis? (f) Can they affect the motion of the loop in any way? Explain. (g) What is the direction of the magnetic force exerted on segment bc? (h) What is the direction of the torque associated with this force about an axis through the origin? (i) What is the torque on segment ad about an axis through the origin? (j) From the point of view of Figure P28.34, once the loop is released from rest at the position shown, will it rotate clockwise or counterclockwise around the x axis? (k) Compute the magnitude of the magnetic moment of the loop. (l) What is the angle between the magnetic moment sector and the magnetic field? (m) Compute the torque on the loop using the results to parts (k) and (l). Figure P28.34
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Two long coaxial copper tubes, each of length L, are connected to a battery of voltage V. The inner tube has inner radius o and outer radius b, and the outer tube has inner radius c and outer radius d. The tubes are then disconnected from the battery and rotated in the same direction at angular speed of radians per second about their common axis. Find the magnetic field (a) at a point inside the space enclosed by the inner tube r d. (Hint: Hunk of copper tubes as a capacitor and find the charge density based on the voltage applied, Q=VC, C=20LIn(c/b) .)