A solid cylindrical straight wire (radius a) has a current I flowing down it. If
ID: 3161121 • Letter: A
Question
A solid cylindrical straight wire (radius a) has a current I flowing down it. If that current is uniformly distributed JUST over the outer surface of the wire (i.e. none is flowing through the "volume of the wire, it's all surface charge), what is the magnitude of the surface current density, |K|? Suppose that current does flow throughout the volume of the wire, but in such a way that the volume current density J grows quadratically with distance from the central axis. What is the formula for J everywhere in the wire? Your result should only be a function of I, a, and s. Note that neither situation i nor ii is physically what happens in normal wires! A DVD has been rubbed so that it has a fixed, constant, uniform surface electric charge density sigma everywhere on its top surface. It is spinning at angular velocity omega about its center (which is at the origin). What is the surface current density |K| at a distance r from the center?Explanation / Answer
(i) K, surface current density = current flowing per unit perpendicular length
K = I/2*a , a is radius of wire
(ii) J= As2 ; s being distance from axis of wire.
I (in wire) = J*area = A*a2**a2.
J= I/perpendicular area of element disc of arbitrary radius s = A*a4*/*s2.
(iii) n = surface charge density = total charge/area of disc.
Angular velocity = w ; v= linear speed at point r = w*r
K = n*v = n*w*r
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