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(Hint: An infinitesimal amount of work is done to align the magnetic moment with the external field. This work rotates the magnetic moment vector through an angle -
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- The force on a magnetic moment z in a nonuniform magnetic field Bz is given by Fz=zdBzdz If a beam of silver atoms travels a horizontal distance of 1 m through such a field and each atom has a speed of 100 m/s, how strong must the field gradient dBz/dz be in order to deflect the beam 1 mm?arrow_forwardQuestion A7 A wire ring of radius a, is placed in an external uniform magnetic field as shown in figure 4 B = B₂+ B₂ where B < 0 and By < 0, and carrying a clock-wise current I. a) Apply the right-hand rule and find the direction of the magnetic moment vector, . b) Derive an expression for the magnitude of the torque on the loop. X Figure 4: A wire ring in an external magnetic field || - [1 marks] marks]arrow_forwardReview a radiused solid ball R with total charge Q made to rotate with angular velocity of w against the z axis. The center point of the ball is clustered with the center point coordinates O(0,0,0). 1. Determine the large magnetic moment of the dipole m from the ball!arrow_forward
- A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0, 0, b) ] (a) Verify that A = Bxr is a vector potential for B, where r = (x, y, 0) (b) Use the Stokes theorem to calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. A Flux(B) = = D B FIGURE 17 A = (8,0,1), B = (8,5, 0), C = (0,5, 0), D = (0, 0, 1), F = (8,0,0)arrow_forwardThe exchange coupling as being responsible for ferromagnetism is not the mutual magnetic interaction between two elementary magnetic dipoles. To show this, calculate (a) the magnitude of the magnetic field a distance of 15 nm away, along a dipole axis, from an atom with magnetic dipole moment 1.8 x 10-23 J/T, and (b) the minimum energy required to turn a second identical dipole end for end in this field. (a) Number i Units (b) Number i Unitsarrow_forwardA circular loop of wire with a radius of 5 cm lies in the xy plane and carries a current of 2 A, counterclockwise when viewed from a point on the positive z axis. What is the direction and the magnetic moment dipole of the loop?arrow_forward
- Inside a square conductive material, a static magnetic field is present H(x,y,z)%3D0 ax-2z ay+ y az (A/m). We are looking to evaluate the current circulating inside the conductive material. The amperian loop is shown in the figure below. The current I(A) using the left or the right side of stokes theorem equals: A(0,1,3) D(0,3,3) Amperian loop B(0,1,1) C(0,3,1) Conductive material N +arrow_forwardin what direction will the roop rotate (x-axis or y-axis) and torque magnitude given that it is a square loop with a side length of 4 cm with a current of 1.3 mA initially at rest and lies fltly within the xy plane with center at origin with a uniform magetic field of (2i +3k)mT and the magnetic moment point of the loop is to the k directionarrow_forwardThe exchange coupling as being responsible for ferromagnetism is not the mutual magnetic interaction between two elementary magnetic dipoles. To show this, calculate (a) the magnitude of the magnetic field a distance of 11 nm away, along a dipole axis, from an atom with magnetic dipole moment 1.9 × 10-23 J/T, and (b) the minimum energy required to turn a second identical dipole end for end in this field.arrow_forward
- Two magnetic systems in thermal contact Consider two isolated systems of noninteracting spins with NA = 4 and NB = 16. Their initial energies are EA = -2µB %3D %3D and Eb= -2µB. What is the most probable macrostate for the composite system?arrow_forwardThe angular momentum of a mass distribution where a differential element particle of mass m with velocity v and located at position r is defined in the form L = dmr x v = dvpr x v, p= nm where n is the number of particles per unit volume and m is its mass. If each of the particles has a charge q, with their movement they constitute a current J = nqv Show that the relationship between the magnetic dipole moment and the angular momentum is L m = 2m where the magnetic moment is defined m = dvr x Jarrow_forwardTwo magnetic systems in thermal contact Consider two isolated systems of noninteracting spins with NA = 4 and NB = 16. Their initial energies are EA = -2µB and EB= -2µB. (a) What is the total number of microstates available to the composite system? (b) If the two systems are now allowed to exchange energy with one another, what is the probability that system A has energy EA? (c) What is the mean value of EA and its relative fluctuations? Calculate the analogous quantities for system В. (d) What is the most probable macrostate for the composite system?arrow_forward
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning