The current density inside a long, solid, cylindrical wire of
radius a = 5.0 mm is in the direction of the central axis
and its magnitude varies linearly with radial distance r
from the axis according to J =
J0r/a, where
J0 = 220 A/m2. Find the magnitude of
the magnetic field at a distance (a) r=0, (b) r = 2.7 mm
and (c) r=5.0 mm from the center.
Consider the cylindrical wire of radius R= 5mm having current
density through
a cross section varies with radial distance ‘r’ as J= (3x 109 A/m4
) r2 , and ‘r’ is
in meters. What is the current through the outer portion of the
wire between
radial distances r=0.75R and r=R.
A uniform current density given by:
J = (A/m2 J ) o az
give rise to a magnetic potential:
A = ( (Wb/m) 4 μo J o x ) 2 + y 2 i.
1) Apply the vector Poisson’s equation to prove the above
statement.
2). Determine H using the expression of A
3). Determine H using the expression of J.
What is the current in a wire of radius R = 3.58 mm if the
magnitude of the current density is given by (a) Ja = J0r/R and (b)
Jb = J0(1 - r/R) in which r is the radial distance and J0 = 5.08 ×
10^4 A/m^2? (c) Which function maximizes the current density near
the wire’s surface?
Find the current density necessary to float a copper wire in
Earth’s magnetic field. Assume the experiment to be done at the
Earth’s magnetic equator in a field of 10?4 T. Use nominal density
of copper in g/cm^3.
A silver wire with resistivity 1.59 x 10^-8 ? x m carries a
current density of 4.0 mm^2. What is the magnitude of the electric
field inside the wire?
A) 0.064 V/m
B) 2.5 V/m
C) 0.040 V/m
D) 0.10 V/m
A current carrying gold wire has diameter of 0.84 mm.
the electric field in the wire is 0.49 V/m. What is
a The current carried by the wire?
b The potential difference between two points in the
wire 6.4 m apart?
c The resistance of a 6.4 m length of this wire.
A 10.3 g wire has a density of 5.9 g/cm3 and a resistivity of
1.51 × 10−7 Ω · m . The wire has a resistance of 106 Ω . How long
is the wire? The wire is made up of atoms with molecular mass 48
g/mol. What is the drift speed of the electrons when there is a
voltage drop of 243.8 V across the wire? Assume there is one
conduction electron per atom. The fundamental charge is 1.602...