4· [14 pts] Consider a thick slab of current. The slab is infinite in (both) x...
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.
4. Thick Current Sheet Current flows in a slab with thickness w that is parallel to the x – y plane and infinite in the x and y directions. The current density in the slab is J = J. Ê in the region –w/2<z 5 w/2. Use Amperes' law to find B above, below, and within the slab. Justify all steps in your derivation and provide a diagram.
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).
An infinite slab of charge of thickness 10m lies on the x-y plane between z = -5m and z=+5m. The charge density, ρ, is 4 C/m3 and is a constant throughout the slab. (HINT: this is similar to what we did in class to find the E-field for an “infinite sheet” of charge… remember the cookie dough and the cookie cutter). a. Use Gauss's Law to find an expression for the Electric Field strength for any point inside the slab (-5m...
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.
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.
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...
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.
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,...
Please show steps B. Magnetostaties: The x-y plane contains an infinite current sheet with surface current density s8Is. Find the magnetic fleld H everywhere in space. Amperian Contour O00o y (a) Use the right-hand rule and make a "Ruestimate" for the magnetic field intensity H both above (z> 0) and below (z<0) this infinite current sheet. (b) Choose an Amperian Contour that encloses the current sheet as shown above and perform the closed path integral of H di around this...