Question

(c) Write Ampere’s law in integral form. Using this form find the volume current density J as a function of distance r from the axis of a radially symmetrical parallel stream of electrons in a wire if the magnetic field inside the stream varies as B(r) = µ0r 2 .Find the total current flowing in the wire with the radius r = R.

Answer #1

Solid cylindrical wire of infinitely length has radius R. I, a
current, is flowing in the z direction. Through the cross section
of the wire, the current flow is uniformly distributed.
1. Find the current density vector J in the wire. Show your
steps and be clear on the formulas.
2. What's the magnitude of the magnetic field at points outside
the wire? Use Ampere’s Law.
3. What's the magnitude of the magnetic field at points inside
the wire? Again,...

The current density inside a long, solid, cylindrical wire of
radius a = 3.6 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 = 420 A/m2. Find the magnitude of
the magnetic field at a distance (a) r=0, (b) r = 2.0 mm
and (c) r=3.6 mm from the center.

1. In Ampere’s law, when we integrate the magnetic field along a
loop, which are summing?
a. the field components that are parallel to the
path elements, at every point along the loop
b. the field components that are perpendicular to the
path elements, at every point along the loop
c. the magnitudes of the field vectors at every point
along the loop
2. Which describes the magnetic field at a point inside a long
wire that...

1. In Ampere’s law, when we integrate the magnetic field along a
loop, which are summing?
a. the field components that are parallel to the
path elements, at every point along the loop
b. the field components that are perpendicular to the
path elements, at every point along the loop
c. the magnitudes of the field vectors at every point
along the loop
2. Which describes the magnetic field at a point inside a long
wire that...

Use Ampere’s Law to determine the magnetic field as a function
of r (distance from the symmetry axis) both inside and outside an
infinitely long cylinder of radius R, carrying a current Iothat
is(show all relevant steps and any symmetry arguments in part a,
then you don’t have to repeat them in part b):
a) uniformly distributed over the surface of the cylinder (i.e.,
at r = R)
b) uniformly distributed throughout the cylinder

A wire of radius R carries a non-uniform current described by
the current density J = A r^3 where r is the radial distance from
the center of the wire
1 write an expression for the total current that flows through
the wire in terms of the parameters A, R, and constants.
2) What is the magnetic field B in the region r < R. Be sure
to specify the direction of the field.
3) A positive charge is moving...

In a conductive and infinite cylindrical wire, the radius R is flowing from right to left, see drawing. The current density across the cross-sectional area of the wire is not uniform but varies by the following expression : J (r) = b · r
Where r is the distance from the center of the cylinder cross-section (radius axis) and b is constant.
A) Calculate the size of the general current flowing in the wire (I).
B) Calculate the magnitude and...

1.
(a) Define a law of electrostatics in integral form that is used to
compute the
electrostatic field E due to a symmetric distribution of charge
within a given volume. State the meaning of the terms in the
defining equation.
(b) A uniformly charged long cylinder of radius a and length L has
total charge q inside its volume.
What is the direction of the electric field at points outside the
cylinder?
Find the electric field inside and outside...

1. Which describes the vector calculation of the Biot-Savart
law?
a. The length element in the direction of the
current is crossed into a vector directed from that element toward
the point of measurement.
b. The length element in the direction of the current
is dotted into a vector directed from that element toward the point
of measurement.
c. The magnetic field vector is crossed into a vector
directed from a current-length element toward the point of...

A long cylindrical wire of radius R, made from a linear material
with a magnetic susceptibility of Xm , carries a volume
current density J = ks ẑ along the z-axis.
For all below please include magnitude and direction:
(a) Find the auxiliary field H, the magnetic field B, and the
magnetization M inside the wire
(b) Find the auxiliary field H, the magnetic field B, and the
magnetization M outside the wire
(c) Find the bound current densities Jb...

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