Permanent Magnet
A permanent magnet in the shape of a right circular cylinder of length L and radius R is oriented so that its symmetry axis coincides with the z-axis. The origin of coordinates is at the center of the magnet. If the cylinder has uniform axial magnetization M, a.) determine U* (z) at points on the symmetry axis, both inside and outside the magnet, and b.) use the results of part a.) to find the magnetic induction Bz at points on the symmetry axis, both inside and outside the magnet.
Homework Answers
I. Determine the magnetic flux density on the axis of uniformly magnetized circular cylinder of a...
I. Determine the magnetic flux density on the axis of uniformly magnetized circular cylinder of a magnetic material. The cylinder has a radius b, length L, axial magnetization M-zMo, and is centered on the z axis. 2. Sketch the magnetic flux lines both inside and outside a cylindrical bar magnet as defined in the previous problem. Additionally, investigate the relationship between B and H inside and outside the magnet.
3. A cylindrical bar magnet has radius a and finite length 2, centered at the origin; it has uniform axial magnetization M. (a) Detail the correspondence with the solenoid in HW 5, #3: Evaluate the m...
3. A cylindrical bar magnet has radius a and finite length 2, centered at the origin; it has uniform axial magnetization M. (a) Detail the correspondence with the solenoid in HW 5, #3: Evaluate the magnetzation surface-current density i and check the value found for the total magnetic dipole moment m against the definition of M as its volume-density. (b) Express B(o and H) on the axis, inside and outside the magnet, in terms of M, I , a, and乙Draw...
3) Didn't I just ask this? A long circular cylinder of radius R carries a magnetization...
3) Didn't I just ask this? A long circular cylinder of radius R carries a magnetization M ksp, where k is a constant, s is the distance from the axis, and ф is the azimuthal unit vector. a) Use ф H- dl = hemet to determine the auxiliary field (H field) both inside and outside of the cylinder b) use H = (110)2-M to determine the magnetic field (B-field) both inside and outside of the cylinder
#6) (25 pts total) An infinitely long cylinder of radius R carries a “frozen-in” magnetization parallel...
#6) (25 pts total) An infinitely long cylinder of radius R carries a “frozen-in” magnetization parallel to the axis M = kpa, where k is a constant and pis the distance from the axis. (a) (12 pts) Calculate all the bound currents. (b) (13 pts) Find the magnetic field, B, inside and outside of the cylinder. (This is for cylindrical coordinates where "s" is the same as “p”)
A bar magnet with magnetic dipole moment 0.6A · m2 lies on the negative x axis
A bar magnet with magnetic dipole moment 0.6A · m2 lies on the negative x axis, as shown in the figure below. A compass is located at the origin. Magnetic north is in the negative z direction. Between the bar magnet and the compass is a coil of wire of radius 3.5 cm, connected to batteries not shown. The distance from the center of the coil to the center of the compass is 8.9 cm. The distance from the center...
Vurpen
(a)The magnetic moment of a macroscopic body is defined as $\int_{V} M d \tau .$ Prove the relationship
$$
\int_{V} \vec{M} d \tau=\int_{V} \vec{r} \rho_{M} d \tau+\oint_{S} \vec{r} \sigma_{M} d a
$$
where $\mathrm{S}$ is the surface bounding $\mathrm{V}$. [Hint: Refer to the similar problem involving polarization $\vec{P}]$ (b) $\mathrm{A}$ permanent magnet in the shape of a sphere of radius $R$ has uniform magnetization $\vec{M}_{0}$ in the direction of the polar axis. determine teh magnetic moment of the magnet from...
18. A loudspeaker is constructed from a circular, concentric permanent magnet that produces a radial magnetic...
18. A loudspeaker is constructed from a circular, concentric permanent magnet that produces a radial magnetic field of flux density B-0.8T, as shown in the front view in Figure 8A. In the circular gap between the poles, a circular coil of radius 16 mm is placed, and attached to a moveable cone which produces the sound at the front of the speaker (see Figure 8B, sectional view). The coil consists of 30 turns of copper wire (only 8 shown in...
An infinitely long circular cylinder carries a permanent magnetization M = ks^2 zˆ. a) Calculate the...
An infinitely long circular cylinder carries a permanent magnetization M = ks^2 zˆ. a) Calculate the bound current densities Jb and Kb. b) Calculate the total current due to Jb circulating around the axis of the cylinder within a section of length ∆z = L, and indicate its direction. (Show your integral explicitly.) c) Calculate the total current due to Kb circulating around the axis of the cylinder within a section of length ∆z = L, and indicate its direction....
A coil of radius R << d with N loops of current I lics in the...
A coil of radius R << d with N loops of current I lics in the xz-plane. The center of the coil is located on the x-axis a distance d from the origin as indicated in the diagram. The bar magnet is still located int he xy-planc but the center of the magnet has been moved along the negative x-axis a distance d. At these locations the magnetic ficld of the coil and bar magnetic exactly cancel at the origin...
I. Determine the magnetic flux density on the axis of uniformly magnetized circular cylinder of a magnetic material. The cylinder has a radius b, length L, axial magnetization M-zMo, and is centered on the z axis. 2. Sketch the magnetic flux lines both inside and outside a cylindrical bar magnet as defined in the previous problem. Additionally, investigate the relationship between B and H inside and outside the magnet.
3. A cylindrical bar magnet has radius a and finite length 2, centered at the origin; it has uniform axial magnetization M. (a) Detail the correspondence with the solenoid in HW 5, #3: Evaluate the magnetzation surface-current density i and check the value found for the total magnetic dipole moment m against the definition of M as its volume-density. (b) Express B(o and H) on the axis, inside and outside the magnet, in terms of M, I , a, and乙Draw...
3) Didn't I just ask this? A long circular cylinder of radius R carries a magnetization M ksp, where k is a constant, s is the distance from the axis, and ф is the azimuthal unit vector. a) Use ф H- dl = hemet to determine the auxiliary field (H field) both inside and outside of the cylinder b) use H = (110)2-M to determine the magnetic field (B-field) both inside and outside of the cylinder
#6) (25 pts total) An infinitely long cylinder of radius R carries a “frozen-in” magnetization parallel to the axis M = kpa, where k is a constant and pis the distance from the axis. (a) (12 pts) Calculate all the bound currents. (b) (13 pts) Find the magnetic field, B, inside and outside of the cylinder. (This is for cylindrical coordinates where "s" is the same as “p”)
18. A loudspeaker is constructed from a circular, concentric permanent magnet that produces a radial magnetic field of flux density B-0.8T, as shown in the front view in Figure 8A. In the circular gap between the poles, a circular coil of radius 16 mm is placed, and attached to a moveable cone which produces the sound at the front of the speaker (see Figure 8B, sectional view). The coil consists of 30 turns of copper wire (only 8 shown in...
A coil of radius R << d with N loops of current I lics in the xz-plane. The center of the coil is located on the x-axis a distance d from the origin as indicated in the diagram. The bar magnet is still located int he xy-planc but the center of the magnet has been moved along the negative x-axis a distance d. At these locations the magnetic ficld of the coil and bar magnetic exactly cancel at the origin...
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