A magnetic dipole with a dipole moment of magnitude 0.0345 J/T is released from rest in a uniform magnetic field of magnitude 51.4 mT. The rotation of the dipole due to the magnetic force on it is unimpeded. When the dipole rotates through the orientation where its dipole moment is aligned with the magnetic field, its kinetic energy is 0.559 mJ. (a) What is the initial angle between the dipole moment and the magnetic field? (b) What is the angle when the dipole is next (momentarily) at rest? (a) Number i Units (b) Number i Units
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- A circular coil of 151 turns has a radius of 1.65 cm. (a) Calculate the current that results in a magnetic dipole moment of magnitude 2.43 A•m?. (b) Find the maximum magnitude of the torque that the coil, carrying this current, can experience in a uniform 30.6 mT magnetic field.A typical magnitude of the external magnetic field in a cardiac catheter ablation procedure using remote magnetic navigation is B = 0.080 T. Suppose that the permanent magnet in the catheter used in the procedure is inside the left atrium of the heart and subject to this external magnetic field. The permanent magnet has a magnetic moment of 0.15 A . m². The orientation of the permanent magnet is 20° from the direction of the external magnetic field lines. (a) What is the magnitude of the torque on the tip of the catheter containing this permanent magnet? mN. m (b) What is the potential energy of the system consisting of the permanent magnet in the catheter and the magnetic field provided by the external magnets? m]A magnetic dipole moment of m = (7.50, -8.38, 4.59) Am² is inside a uniform magnetic field of B = (3.34, -6.77, 6.79) T. What is the potential energy of the dipole? (a) What is the angle between the magnetic dipole moment vector and the magnetic field vector? (b) What is the magnitude of the torque acting on the dipole?
- Suppose that the dipole moment associated with an iron atom of an iron bar is 2.8 x 1023 J/T. The bar is 5.2 cm long and has a cross-sectional area of 1.5 cm2. Two-thirds of the atoms have their dipole moment in one directions and remaining one-third have their dipole moment in the opposite direction. What torque (in N*m) must be exerted to hold this magnet perpendicular to an external field of 1.2 T? (The density of iron is 7.9 g/cm3 and its molar mass is 55.9 g/mol. Avogadro's number is 6.022*1023 atoms/mol.)A magnetic dipole with a dipole moment of magnitude 0.016 J/T is released from rest in a uniform magnetic field of magnitude 58 mT. The rotation of the dipole due to the magnetic force on it is unimpeded. When the dipole rotates through the orientation where its dipole moment is aligned with the magnetic field, its kinetic energy is 0.60 mJ. (a) What is the initial angle between the dipole moment and the magnetic field? _____________°(b) What is the angle between the dipole moment and the magnetic field when the dipole is next (momentarily) at rest? ______________°Doubly-ionized particles with an atomic mass of 59.4 u are moving due N at a speed of 7.78 x 105 m/s when they enter a uniform magnetic field of strength, B = 35.5 mT. The ions, which are moving perpendicular to the field, follow a circular path of radius, r, and travel north a distance, h = 2.02 m, before leaving the field at an angle, 8, as shown in the figure. (a) What is the radius of the ions' circular path? r = 6.793 m (b) At what angle do the ions leave the field? 0 = 73.44 x h 0 2
- A particle with a mass of 5.00 x 10-16 kg and a charge of 21.0 nC starts from rest, is accelerated through a potential difference AV, and is fired from a small source in a region containing a uniform, constant magnetic field of magnitude 0.600 T. The particle's velocity is perpendicular to the magnetic field lines. The circular orbit of the particle as it returns to the location of the source encloses a magnetic flux of 15.0 µWb. (a) Calculate the particle's speed. m/s (b) Calculate the potential difference through which the particle was accelerated inside the source. VA magnetic dipole with a dipole moment of magnitude 0.0306 J/T is released from rest in a uniform magnetic field of magnitude 57.6 mT. The rotation of the dipole due to the magnetic force on it is unimpeded. When the dipole rotates through the orientation where its dipole moment is aligned with the magnetic field, its kinetic energy is 0.573 mJ. (a) What is the initial angle between the dipole moment and the magnetic field? (b) What is the angle when the dipole is next (momentarily) at rest?Chapter 29, Problem 057 A student makes a short electromagnet by winding 430 turns of wire around a wooden cylinder of diameter d = 4.5 cm. The coil is connected to a battery producing a current of 3.1 A in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance z >> d will the magnetic field have the magnitude 7.0 µT (approximately one-tenth that of Earth's magnetic field)?
- Find the torque exerted on a small magnetic dipole with a magnetic moment of 1.9 ✕ 10−4 A · m2 along the +y-direction in a region of magnetic field of 1.6 T oriented along the +z-axis. Find the magnitude and direction.A 1.00 C charge enters a uniform magnetic field. The magnetic field vector has the following components: 1.00 T in the x-direction, 2.00 T in the y-direction, and 3.00 T in the z-direction. The particle enters the magnetic field with a constant velocity whose components are as follows: 4.00 m/s in the x-direction, 5.00 m/s in the y-direction, and 6.00 m/s in the z-direction. - What are the components of the magnetic force in the particle? (Fx, Fy, and Fz) - What is the magnitude of the magnetic force?A square loop with 10 turns and a side length of 5.0 cm lies flat on a tabletop. The loop carries a current of 2.0 A that goes counterclockwise when viewed from above while looking down on the table. (a) What is the magnitude and direction of the magnetic moment of the loop? (b) If there is a uniform magnetic field with magnitude 0.75 T at the location of the loop that heads down through the tabletop and makes an angle of 60 degrees with the surface of the tabletop, then answer the following: (i) what is the magnitude of the net magnetic force on the loop, and (ii) what is the magnitude of the net torque on the loop? (c) Include a diagram of the situation.