Question

1. (a) A solid cylindrical straight wire of vadius a has a current I. flowng down t Eftha cument untfermly distributed over the outer surface of the wire (mone ts flowm throug)h the volume of the wre: t is all surface charge», what ts the surface current densty (b) Suppose that curfent does flow throughout the volume of the wtre, n such a way that the volume current density J grows quadratically wth drstance fram the central a*>s what then rs the forma fer everywhere m the wire? c) A DVD has been ubbed so that has a fixed constart uniform. Surface electric chame density σ everwhere on ts top surface. Its spinningat angular velociy ω about rts certerC which is at the origin). h s the surface curert dengHy K at a distance r fom the cevher? (d) A sphere radins R, total charge G unformly distributed th ughont the volume) is spinning at angular velocity ω obout Ns center Cart oriqin) uhut|s the Volume current denny ริ otany point cre. in the phere* te) A vey thin plaplic rnghas a constant Imear charge densty and total charge a. "The ring has radius R and-+x Spinnimg at angular velecy w about an axts through its center at orngin) and perpendicular to the plane of the ring what is the current L n terms of gven quarnttes? f) Use the current densty K you obtatned rom c) for a DVD and And the mnettc field всео,Z) at any distance z dnectly above the orngm Does your answer seem reasonable Please check t, wth unHs, and some lim behavrors, what do you expect rf R→o3 co → o? Z→oo?

Answer 1

1. . radius of the wire = a

consider a lengh of 1 mt of the wire

surface area A = 2a sq.m

current flowing through the wire = I

entire current flows through the surface

current density = I/2a A/sq.m

2. consider a cylindrical shell fo radius r and thickness dr and of length 1 m

volume of the shell dV = 2rdr

Let J = kr² , given J grows quadratically with r

current through the shell

dI = JdV = 2kr³dr

Total current through the wire

       

             = ka⁴/2

k = 2I/a⁴

current density J(r) = kr² = 2Ir²/a⁴

3. . Surface current density is the current flowing through a unit width perpendicular to the flow of current

consider a strip of width dr and radius r

length of the strip moving per unit time = r

charge on the strip dq= rdr

current I = dq/dt = rdr

surface current density K = rdr/dr = r