Question

Radial Hall Effect An infinitely long cylindrical conductor carries a constant current with density jz(r).

(a) Despite Ohm’s law, compute the radial electric field Er (r) that ensures that the radial component of the

Lorentz force is zero for every current-carrying electron.

(b) The source of Er (r) is ρ(r) = ρ+ + ρc(r) where ρ+ comes from a uniform distribution of immobile

positive ions and ρc(r) = jz(r)/v comes from electrons with velocity v. Show that ρc(r) = ρc

=

−ρ+/(1 − v2/c2). Do not use special relativity.

Answer #1

An infinitely long solid cylindrical cable (radius R, centered
on the z-axis) carries a volume current ?⃗ = (??^5) ?̂, The cable
is surrounded by a concentric, infinitely long solenoid (radius 3R,
n turns /m) carrying a current ?0.
a. Find expressions for the magnetic field in all regions of
space.
b. Graph the field as a function of position along the
x-axis.
c. Find the force on a segment of wire from (x = 4R, y = 0, z...

An infinitely long solid cylindrical cable (radius R, centered
on the z-axis) carries a volume current ?⃗ = (??^5) ?̂, The cable
is surrounded by a concentric, infinitely long solenoid (radius 3R,
n turns /m) carrying a current ?0.
a. Find expressions for the magnetic field in all regions of
space.
b. Graph the field as a function of position along the
x-axis.
c. Find the force on a segment of wire from (x = 4R, y = 0, z...

10. A spherical conductor of radius R = 1.5cm carries the charge of
45μ,
(a) What is the charge density (ρ) of the sphere?
(b) Calculate the electric field at a point r = 0.5cm from the
center of the sphere.
(c) What is the electric field on the surface of the sphere?
11. Two capacitors C1 and C2 are in series with a voltage V across
the series combination.
Show that the voltages V1 and V2 across C1 and...

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