Concentric conducting spherical shells carry charges Q and -Q , respectively (see below). The inner shell has negligible thickness. Determine the electric field for (a) r < a ; (b) a < r < b ; b < r < c ; and (d) r > c .
Concentric conducting spherical shells carry charges Q and -Q , respectively (see below). The inner shell has negligible thickness. Determine the electric field for (a) r < a ; (b) a < r < b ; b < r < c ; and (d) r > c .
Concentric conducting spherical shells carry charges Q and -Q, respectively (see below). The inner shell has negligible thickness. Determine the electric field for (a)
r
<
a
;
(b)
a
<
r
<
b
;
2. (a) Suppose you design an apparatus in which a uniformly charged disk of
radius R is to produce an electric field. The field magnitude is most important
along the central perpendicular axis of the disk, at a point P at distance 4.40R
from the disk (see Figure (a)). Cost analysis suggests that you switch to a ring
of the same outer radius R but with inner radius R/4.40 (see Figure (b)).
Assume that the ring will have the same surface charge density as the original
disk. If you switch to the ring, by what part will you decrease the electric field
magnitude at P?
(a)
(b)
(b) In the figure, four long straight wires are perpendicular to the page, and
their cross sections form a square of edge length a = 115 mm. Each wire carries
8.00 A, and the currents are out of the page in wires 1 and 4 and into the page
in wires 2 and 3. In unit-vector notation, what is the net magnetic force per
meter of wire length on wire 4?
ia
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Textbook Problem
When an uncharged conducting sphere of
radius a is placed at the origin of an xyz
coordinate system that lies in an initially
uniform electric field E →
= E 0k^,
the
resulting electric potential is Vx, y, z) = Vo for
points inside the sphere and
V (x, y, z)=V0 - E 0 z+ E 0 a 3 z (x 2 + y 2 + z 2
) 3/2
for points outside the sphere, where Vo is the
(constant) electric potential on the conductor.
Use this equation to determine the x, y, and z
components of the resulting electric field (a)
inside the sphere and (b) outside the sphere.
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Two circular disks spaced 0.50 mm apart form a parallel-
plate capacitor. Transferring 3.00×109 electrons from one
disk to the other causes the electric field strength to be
1.00×105 N/C.
[
What are the diameters of the disks?
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