18.1 A long straight wire of radius a is oriented with its center along the z...
4. A steady current I flows down a long cylindrical wire of radius a. (a) Find the magnetic field, both inside and outside the wire, if the current is uniformly dis- tributed over the outside surface of the wire. (b) Find the magnetic field, both inside and outside the wire, if the current is distributed in such a way that the current density J is proportional to s2, where s is the distance from the axis. (c) Show that your answers to (a)...
5.22 A long cylindrical conductor whose axis is coincident with the z axis has a radius a and carries a current characterized by a current density J żJo/r, where Jo is a constant and r is the radial distance from the cylinder's axis. Obtain an expression for the magnetic field H for (a) 0<r Sa (b) r > a
(a) (10 marks] A straight wire along the ź direction with a circular cross-section of radius R, carries a total current of magnitudel, and the magnitude of the current density varies as I = ks 2 where k is a constant and s is the radial distance from the axis of the wire. i) Express the constant k in terms of I and R. Show that the magnetic field inside the wire can be expressed as B = 80. Find...
2. A modified coaxial cable consists of a solid cylinder (radius 'a') with a uniform current density and a concentric cylindrical conducting thin shell (radius 'b'). The outer and inner current have an equal magnitude, but are opposite in direction. Io (along outside) (along the axis) (off-axis view) In terms of radial distance 'r', and the relevant parameters in the diagram above, A) Derive an expression for the magnetic field inside the solid cylinder (r <a) B) Derive an expression...
5-15 Exercises: 5.16. A very long, straight conductor located along the z axis has a circular cross section of radius 10 cm. The conductor carries 100 A in the z direction which is uniformly distributed over its cross section. Find the magnetic field intensity (a) inside the conductor and (b) outside the conductor. Sketch the magnetic field intensity as a function of the distance from the center of the conductor. 5-15 Exercises: 5.18. A fine wire wound in the form of...
Also, what is the difference between motional EMF and transformer EMF? Explain briefly. A long, straight, solid cylindrical conductor with a radius of a is shown above. The surrounding medium is free space. There is a total current lo carried by this conductor directed into the page What is the current density vector J? What is the magnetic field intensity vector H1 inside the conductor (r<a)? What is the magnetic field intensity vector H2 outside the conductor (r>a)? Ir Ir
10 (b) A long straight metal wire of radius a is directed along the z axis and is surrounded by a coaxial metal cylinder of radius b, thus forming a coaxial waveguide. Consider an electromagnetic wave in this waveguide, with the electric field given by where C is a constant, s is the radius-vector in cylindrical coordinates, and w is the angular frequency of the wave (i) Show that on the inner surface of the outer cylinder, the wave satisfies...
(2) 4.[4pts) An infinitely long cylinder of radius R carries NO free current but magnetization M=ks, where k > 0 is a constant and s is the cylindrical radius from the axis. Find the magnetic field B due to M both inside and outside of the cylinder.
2. An infinitely long wire with linear charge density - is centered inside an in- finitely long cylinder with surface charge density o and radius a, oriented along the z-axis. (a) Use Gauss's Law to determine the electric field between the wire and cylinder. (b) What must o be, such that the electric field is zero outside the cylinder? (c) An external magnetic field, Bert = Bert 2, is now applied. What is the total angular momentum per unit length...
A long, cylindrical wire of radius R has a current density J(r) = Jo(1 – r2/R2) for distances where r < R and J(r) = 0 for r < R where r is the distance from the center of the wire’s axis. Find the magnetic field strength inside (r < R) and outside (r > R) the wire. Sketch the magnetic field strength as a function of distance r from r = 0 to r = 2R. Find the location...