Two square plates of sides é are placed parallel to each other with separation d as suggested in Figure P26.65. You may assume d is much less than €. The plates carry uniformly distributed static charges +Q. and -Qo. Á block of metal has width €, length €, and thickness slightly less than d. It is inserted a distance x into the space between the plates. The charges on the plates remain uniformly distributed as the block slides in. In a static situation, a metal prevents an electric field from penetrating inside it. The metal can be thought of as a perfect dielectric, with « → 0. (a) Calculate the stored energy in the system as a function of x. (b) Find the direction and magnitude of the force that acts on the metallic block. (c) The area of the advancing front face of the block is essen- tially equal to ld. Considering the force on the block as acting on this face, find the stress (force per area) on it. (d) Express the energy density in the electric field between the charged plates in terms of Qo, €, d, and eg. (e) Explain how the answers to parts (c) and (d) compare with each other.
Two square plates of sides é are placed parallel to each other with separation d as suggested in Figure P26.65. You may assume d is much less than €. The plates carry uniformly distributed static charges +Q. and -Qo. Á block of metal has width €, length €, and thickness slightly less than d. It is inserted a distance x into the space between the plates. The charges on the plates remain uniformly distributed as the block slides in. In a static situation, a metal prevents an electric field from penetrating inside it. The metal can be thought of as a perfect dielectric, with « → 0. (a) Calculate the stored energy in the system as a function of x. (b) Find the direction and magnitude of the force that acts on the metallic block. (c) The area of the advancing front face of the block is essen- tially equal to ld. Considering the force on the block as acting on this face, find the stress (force per area) on it. (d) Express the energy density in the electric field between the charged plates in terms of Qo, €, d, and eg. (e) Explain how the answers to parts (c) and (d) compare with each other.
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Transcribed Image Text:65. Two square plates of sides { are placed parallel to
each other with separation d as suggested in Figure
P26.65. You may assume d is much less than e. The
plates carry uniformly distributed static charges +Q,
and -Qo. Á block of metal has width €, length €, and
thickness slightly less than d. It is inserted a distance
x into the space between the plates. The charges on
the plates remain uniformly distributed as the block
slides in. In a static situation, a metal prevents an
electric field from penetrating inside it. The metal
can be thought of as a perfect dielectric, with x → *.
(a) Calculate the stored energy in the system as a
function of x. (b) Find the direction and magnitude
of the force that acts on the metallic block. (c) The
area of the advancing front face of the block is essen-
tially equal to ld. Considering the force on the block
as acting on this face, find the stress (force per area)
on it. (d) Express the energy density in the electric
field between the charged plates in terms of Qo, €, d,
and eg. (e) Explain how the answers to parts (c) and
(d) compare with each other.
Qo
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