Consider two parallel copper plates both 1m² in area. The lower plate is charged with 4uC of charge and the upper plate with -4µC of charge. (a) Determine the charge density o on each plate. (b) Neglecting edge effects (assuming a homogeneous field between the plates), show that the electric field can be expressed in the form E = E02 using Gauss' Law. Determine the value of Eo. (c) Consider now the addition of an open hemispherical surface (no base) of radius R between the two plates in the orientation shown in Fig. 1. What is the expression for electric flux through this surface? Given R = 3cm, what is the value of the flux?

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Consider two parallel copper plates both 1m? in area. The lower plate is charged with 4µC of charge and
the upper plate with -4µC of charge.
(a) Determine the charge density o on each plate.
(b) Neglecting edge effects (assuming a homogeneous field between the plates), show that the electric
field can be expressed in the form E = Eoê using Gauss' Law. Determine the value of Eo.
(c) Consider now the addition of an open hemispherical surface (no base) of radius R between the two
plates in the orientation shown in Fig. 1. What is the expression for electric flux through this
surface? Given R = 3cm, what is the value of the flux?
R
FIGURE 1
(d) Consider now a rotation of the hemispherical surface of 90° about the x-axis. What is the the new
flux through the surface?
(e) Following (d), a point charge q is placed at the origin of the hemispherical surface. Assume that
small enough that it does not affect the charge density on the plates. What is the new flux through
the hemisphere?
is
Transcribed Image Text:Consider two parallel copper plates both 1m? in area. The lower plate is charged with 4µC of charge and the upper plate with -4µC of charge. (a) Determine the charge density o on each plate. (b) Neglecting edge effects (assuming a homogeneous field between the plates), show that the electric field can be expressed in the form E = Eoê using Gauss' Law. Determine the value of Eo. (c) Consider now the addition of an open hemispherical surface (no base) of radius R between the two plates in the orientation shown in Fig. 1. What is the expression for electric flux through this surface? Given R = 3cm, what is the value of the flux? R FIGURE 1 (d) Consider now a rotation of the hemispherical surface of 90° about the x-axis. What is the the new flux through the surface? (e) Following (d), a point charge q is placed at the origin of the hemispherical surface. Assume that small enough that it does not affect the charge density on the plates. What is the new flux through the hemisphere? is
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