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4. Thick Current Sheet Current flows in a slab with thickness w that is parallel to...
An infinite slab of conductive material with thickness w sits perpendicular to the z-axis, centered...
An infinite slab of conductive material with thickness w sits perpendicular to the z-axis, centered on the xy-plane, carrying a uniform current density J in the Y direction. The current density is increasing in strength at a linear rate y Find the magnitude and direction (CW or CCW around the x-axis) of the current induced in a rectangular conductive ring of total resistance R that rests in the yz-plane outside the slab, if its area is A. Answer in terms...
4· [14 pts] Consider a thick slab of current. The slab is infinite in (both) x...
4· [14 pts] Consider a thick slab of current. The slab is infinite in (both) x and y, but finite in z. The slab has a thickness of 2h, i.e. it runs from z =-h to z = +h). Let's assume that the current is flowing in the +a-direction, and is uniform in the x and y dimensions, but J depends on height linearly, ie. J = JolzX inside the slab (but is 0 above or below the slab). Find...
An infinite horizontal slab of thickness 2w is perpendicular to the z-axis and centered on the...
An infinite horizontal slab of thickness 2w is perpendicular to the z-axis and centered on the xy-plane. It carries a uniform current density J in the x-direction. There is a cylindrical hole in the slab with radius w centered on the x-axis. Find the B-field a distance z from the origin along the z-axis such that z<w. Answer in terms of µ.
2. A thick slab, infinite in extent along r and y, has faces at th. Electric...
2. A thick slab, infinite in extent along r and y, has faces at th. Electric current flows within this slab with uniform current density Jox. Using Ampère's Law, find the magnetic field measured by an observer at Cartesian position (0, 0, z). (There are three regions to consider here: below the slab, within the slab, and above the slab.) Treat this as a question from Chapter 5, i.e., assume that the slab's material is non-magnetic.
A slab of insulating material has thickness 2d and is oriented so that its faces are...
A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x=d and x=?d. The y- and z-dimensions of the slab are very large compared to d and may be treated as essentially infinite. Let the charge density of the slab be given by ?(x)=?0(x/d)2 where ?0 is a positive constant. Part B Using Gauss's law, find the magnitude of the electric field due to the...
Use Ampere’s Law to find the magnetic field of an infinitely large slab and current with...
Use Ampere’s Law to find the magnetic field of an infinitely large slab and current with current density J0 i hat. The slab is infinite in the x and y directions, but has a finite thickness t in the z direction. Do this for both (a) inside at the point p(0, 0,-t/4) and (b) outside at the point p(0,0,4t).
Example 5 reads: We consider an infinite slab of a conducting material with magnetic susceptibility xM carring a certain current distribution. The slab is parallel to the xy plane, between z--a andz-...
Example 5 reads: We consider an infinite slab of a conducting material with magnetic susceptibility xM carring a certain current distribution. The slab is parallel to the xy plane, between z--a andz-a. It carries a free volume current density J, (z) -(Joz/a)i which is plotted in Fig 9.12. Above the xy plane the current is out of the page, below it is into the page, and the integrated current density is 0. Outside the slab is vacuum. What are H,...
Imagine a slab of current that is infinite in x and y but finite in z...
Imagine a slab of current that is infinite in x and y but finite in z with a current density ?J. The slab has a thickness 2h (it runs from z = ?h to z = +h). Assuming the current is still in the x direction and is uniform in the x and y dimensions, but depends linearly on the height (J = J0|z|xˆ) inside the slab. Find the magnetic field everywhere in space, including inside the slab.
QUESTION 7 A slab of insulating material has thickness 2d, with d = 1.98 cm, and...
QUESTION 7 A slab of insulating material has thickness 2d, with d = 1.98 cm, and is oriented so that its faces are parallel to the yz-plane and given by the planes x = 1.98 cm and x = -1.98 cm. The y- and z-dimensions of the slab are very large compared to d and may be treated as essentially infinite. The slab has a uniform positive charge density ρ = 1.65 μC/m3. Using Gauss’s law, find the magnitude of...
9. (20 points) Suppose you have an infinite sheet of thickness d, the bottom lying at...
9. (20 points) Suppose you have an infinite sheet of thickness d, the bottom lying at y = 0 in the x-z plane, that carries a current density described by ] = J. ł, as shown in the image below. d j = Jože ---- I. (4 points) Describe this current density (i.e., it's direction in the image and how it is distributed in the slab). (16 points) Find the magnetic field, B, everywhere. II.
4· [14 pts] Consider a thick slab of current. The slab is infinite in (both) x and y, but finite in z. The slab has a thickness of 2h, i.e. it runs from z =-h to z = +h). Let's assume that the current is flowing in the +a-direction, and is uniform in the x and y dimensions, but J depends on height linearly, ie. J = JolzX inside the slab (but is 0 above or below the slab). Find...
2. A thick slab, infinite in extent along r and y, has faces at th. Electric current flows within this slab with uniform current density Jox. Using Ampère's Law, find the magnetic field measured by an observer at Cartesian position (0, 0, z). (There are three regions to consider here: below the slab, within the slab, and above the slab.) Treat this as a question from Chapter 5, i.e., assume that the slab's material is non-magnetic.
Example 5 reads: We consider an infinite slab of a conducting material with magnetic susceptibility xM carring a certain current distribution. The slab is parallel to the xy plane, between z--a andz-a. It carries a free volume current density J, (z) -(Joz/a)i which is plotted in Fig 9.12. Above the xy plane the current is out of the page, below it is into the page, and the integrated current density is 0. Outside the slab is vacuum. What are H,...
9. (20 points) Suppose you have an infinite sheet of thickness d, the bottom lying at y = 0 in the x-z plane, that carries a current density described by ] = J. ł, as shown in the image below. d j = Jože ---- I. (4 points) Describe this current density (i.e., it's direction in the image and how it is distributed in the slab). (16 points) Find the magnetic field, B, everywhere. II.
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