The idea here is to evaluate hew much of the magnetic freld surroanding a coppee

Question

The idea here is to evaluate hew much of the magnetic freld surroanding a coppee wire casrying 1 Amp AC is due to theceal (conventional) cucrent, compaed to bhe contribution of the displacement cuecent (pcepoctional to the time cate of change of the electeic Flux). J Given, a coppee wice with cesistty p, radius R, careging AC with uniform eusrent use Maxvelli eguation B d to find the megnctic feld B a a function of time at the radial distance rA. use the concept E,oJs /A to get an expression foc ? , and, of coucse # B 2? r as usual. rma 1 3 r 1a mm.ooi5 m ??? 8.85x102,/nm

Explanation / Answer

1. given copper wire

io = 1 A

resistivuty = rho

radius R

AC current

J = i/A = Jo*sin(wt)

A = pi*R^2

form maxwells 4th law

B*2*pi*r = muo(i + epsilon*phie')

phie = rho*J*A = rho*Jo*sin(wt)*A

phie' = rho*Jo*w*cos(wt)*A

B*2*pi*r = muo(io + epsilon*rho*io*w*cos(wt))

rho = 1.69*10^-8 ohm m

R = 0.00050 m

io = 1 A

w = 120*pi*rad /s

r = 0.0015 m

hence

B = 1.333*10^-4(1 + 5.638*10^-17*cos(120*pi*t))

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