Problem 4, 30 marks The infinitely long conducting cylinder of radius R carries the volume current...
Q-2) The infinitely long cylinder volume r < a carries a steady electric current of unknown density JAmps/m2) oriented through z direction = Jêz) as shown in the figure. There is no current outside of the cylinder. All space is vacuum. The magnetic flux density vector for r < a is given as B = epHoGr3 Tesla). Here, G is a constant. a) Find j b) Find B forr a Ho Ho Figure 2. The geometry of the problenm Q-2)...
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....
2. A solid cylinder of radius R1 and permeability u1 has a uniform surface current density K = K2 at its surface, where 2 is the axis of the cylinder. The cylinder is covered by a coaxial cylindrical shell of inner radius R1, outer radius R2 made of a material of permeability H2. The cylindrical shell has no free current. a) Calculate H, B and M in all three regions 0 < r < R1, R1 < r < R2,...
An infinitely long, straight, cylindrical wire of radius R carries a uniform current density J. Using symmetry and Ampere's law, find the magnitude and direction of the magnetic field at a point inside the wire. For the purposes of this problem, use a cylindrical coordinate system with the current in the +z-direction, as shown coming out of the screen in the top illustration. The radial r-coordinate of each point is the distance to the central axis of the wire, and...
Question 3: A long hollow cylinder with radius R carries a time-dependent surface current density K(t) = Kosin(wt) $ (see figure below). The current K(t) varies slowly enough that we are still in the quasistatic approximation. (15 points) KO a) Find the magnetic field B(1), magnitude and direction inside and outside the cylinder. (4 points) b) Find the induced electric field E(t), magnitude and direction, inside and outside the cylinder (8 points) c) Find the displacement current Jinside and outside...
An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as p po (a-where po a and b are positive constants and ris the distance from the axis of the cylinder. Use Gauss's law to determine the magnitude of the electric field at radial distances (a) r< R and (b)r>R
3-28. A very long, nonmagnetic conductor (,-) of radius a carries the static current I as shown. The conductor is surrounded by a cylindrical sleeve of nonconducting magnetic material with a thickness extending from ρ-; a top-b and the permeability μ. The surrounding region is air. (a) Make use of symmetry and Ampère's law (3-66) to find H and B in the three regions (Label the closed lines employed in the proof, depicting H in the proper sense on each...
A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is J⃗ . The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship J⃗ =2I0πa2[1−(ra)2]k^forr≤a=0forr≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and I0 is a constant having units of amperes. A)Using Ampere's law, derive an expression for the magnitude of the magnetic field...
An infinitely long cylinder with axis aloong the z-direction and radius R has a hole of radius a bored parallel to and centered a distance b from the cylinder axis (a+b<R). The charge density is uniform and total charge/length is placed on the cylinder. Find the magnitude and direction of the electric field in the hole.
Problem 4 (20 points): A long, solid conducting cylinder of radius R has a current density within it described by: (r)-C( ) for r< R where C is a constant to be determined. The total current running through the whole cylinder is I. a) Calculate an expression for the constant C, given that the total current is I. (Hint: the current density is not uniform.) b) Why can Ampere's law be used here, and what Amperian loop is appropriate? c)...