9. (20 points) Suppose you have an infinite sheet of thickness d, the bottom lying at...
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.
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· [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 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...
Consider an infinite slab of thickness 2a and uniform volume charge density ρ. This is essentially an infinite plane with a non-negligible thickness. Since the planar symmetry involves:艹-2 reflection symmetry, as well as the translation symmetry along the and y direc- tions, we place the origin at a point on the midplane of the slab. In other words, the midplane corresponds to oo = 0 (i.e., the ry plane) and the surfaces of the slab are at a (a) Use...
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...
5. (4 points) A metal disk of radius a, thickness d, and conductivity o is located in the xy plane, centered at the origin. There is a time-dependent uniform magnetic field B(t) = B(t)2. Determine the induced current density J(r,t).
3. Infinite conductor a) Consider a straight conductor (infinite length) which carries a total current I in the direc- tion of the z axis. Calculate the magnetic induction Ē(7) using the Biot-Savart law. Hint The current density is given by j = 1S(x)6(y)ë^ b) Explicitly check the result from the previous task by calculating the magnetic induction B(F) using the symmetry of the problem and applying Stoke's theorem onto Maxwell's equation of magnetostatics V x B = 407 c) Now,...
Mugnetostaties: The -y plane contains an infinite current sheet with surfiace demsity / Find the manette field n everywhere in space. Amperian Contour a hand make istinatc" for-ths magaeic neld ineity bh above (z > 0) and below (z < 0) this infinite current sheet. perform the closed path integral of N dl around this contour Amperian Contour (b) Choose an Amperian Contour that encloses the current sheet as shown above and (o Calculate the total current fnowing through the...
A hollow, circular cylindrical conductor in freespace of infinite length. The inner and outer radius are b and c respectively, from the center z axis. It carries a current I in z direction. (a) Find the vector current density J. (b) Use Ampere's Law to find the magnetic field B and H outside the conductor(r>c). (c) Find B inside the hollow interior(r<b). (d) Find B in the conductor(b<r<c).