(III) An electric field is given by E = E x 0 e − ( x + y a ) 2 i ^ + E y 0 e − ( x + y a ) 2 j ^ , where E x 0 = 50 N/C, E y 0 = 25 N/C, and a = 1.0 m. Given a cube with sides parallel to the coordinate axes, with one corner at the origin (as in Fig. 22–48), and with sides of length 1.0 m, estimate the flux out of the cube using a spreadsheet or other numerical method. How much total charge is enclosed by the cube?
(III) An electric field is given by E = E x 0 e − ( x + y a ) 2 i ^ + E y 0 e − ( x + y a ) 2 j ^ , where E x 0 = 50 N/C, E y 0 = 25 N/C, and a = 1.0 m. Given a cube with sides parallel to the coordinate axes, with one corner at the origin (as in Fig. 22–48), and with sides of length 1.0 m, estimate the flux out of the cube using a spreadsheet or other numerical method. How much total charge is enclosed by the cube?
E
=
E
x
0
e
−
(
x
+
y
a
)
2
i
^
+
E
y
0
e
−
(
x
+
y
a
)
2
j
^
,
where Ex0 = 50 N/C, Ey0 = 25 N/C, and a = 1.0 m. Given a cube with sides parallel to the coordinate axes, with one corner at the origin (as in Fig. 22–48), and with sides of length 1.0 m, estimate the flux out of the cube using a spreadsheet or other numerical method. How much total charge is enclosed by the cube?
É = Eox cos(wt)ax + Eoy cos(wt + 8)ay
a) Why is the 8 in the equation?
b) Suppose
Eox = Eov = E, = 1
Ох
For this case, plot the magnitude and direction of the electric field vector in
the x-y plane for
5п Зп 7т
T,
4
π π3π
wt =
4'?'7,2 radians
4
Or
wt = [0,45,90,135,180,225,270,315,360] degrees
And
i)
ii)
8 = 0
8 =
2
Consider the following figure. (If you need to use ∞ or -∞, enter INFINITY or -INFINITY, respectively.)
(a)
(b)
0
-2q
+9
5
5
+9
-29
+3q
10
10
+q
x (cm)
x (cm)
-9
(a) Find the total electric field in N/C at x = 1.00 cm in part (b) of the figure above given that q = 5.00 nC.
N/C
(b) Find the total electric field in N/C at x = 10.70 cm in part (b) of the figure above. (Include the sign of the value in your answer.)
N/C
(c) If the charges are allowed to move and eventually be brought to rest by friction, what will the final charge configuration be? (That is, will there be a single charge, double charge, etc., and what
will its value(s) be? Use the following as necessary: q.)
Consider the following figure. (If you need to use so or-, enter INFINITY or -INFINITY, respectively.)
(a)
(6)
0
0
-20
+9
5
5
-q
-29
+3q
10
10
+9
x (cm)
x (cm)
-9
(a) Find the total electric field in N/C at x 1.00 cm in part (b) of the figure above given that q=1.00 p
N/C
(b) Find the total electric field in N/C at x 12.70 cm in part (b) of the figure above. (Include the sign of the value in your answer.)
N/C
(c) If the charges are allowed to move and eventually be brought to rest by friction, what will the final charge configuration be? (That is, will there be a single charge, de
value(s) be? Use the following as necessary: q.)
Chapter 22 Solutions
Physics for Scientists and Engineers with Modern Physics
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