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A hypothetical closed surface is
made by attaching a smoothly dis-
torted hemispherical surface (2) of
radius “R” to a flat circular base
plate (1) also of radius “R” as shown
in cross section at left. The closed
surface is immersed in a constant
horizontal electric field (E) and it
Ã¢â‚¬â€ encloses no charge.
a. What is the flux of the (E) through the closed surface?
b. What is the flux of the (E) through the back surface (1)?
c. What is the flux of the (E) through the front surface (2)?
(Hint: make use of 0.
closed surface (0)zuface panels)
A hypothetical infinitely long (i.e.
L 00) closed semicircular cylindri-
cal shell surface has its axis aligned
on the (z) axis ; the shell has an in-
ner radius of “r” and an outer ra-
dius of “R”. Note that we can as-
sume the shell to be enclosed by
+X four surfaces (1,2,3 and 4) as indica-
ted in the figure. An infinite line of
charge (+ ) runs along the (z) axis
thus coinciding with shell’s axis.
Note that in this problem you will have to use the inte-
gral definition of flux for each surface:
Q = SE-nda
where “M” the outward unit normal vector.
a. What is the flux of the electric field through each of the four
enclosing “surface panels” (i.e. the surfaces 1, 2, 3 and 4)?
b. Using the fact that closed surface
the flux of the electric field through the shell.
Use Gauss’s Law to redo part b.
The figure at left shows a cross sec-
tion of a solid nonconducting sphere
(radius = R = 0.80 m) which has a
a total positive charge (Q) of uniform-
ly distributed throughout its volume
such that it has a constant charge
per unit volume of p = + 64 ucoul/m3.
a. What is the value of the charge (Q) in the sphere?
b. Derive an expression (in terms of p) for the magnitude of the
electric field in the region Osr R and then calculate its value
at the point r = 5.0 m.
e. Referring to part d, convert your expression for (E) from one
in terms of (o) to one in terms of (Q).
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