Download ectric field strength

=
0.48 mC = 4.8 x 10
1
.
C
q
=
2
0.48mC—4.8X10C
= 12.3km1.23X iO
1
r
m
4
N•
I
C
kc = 8.99 x i0 2
m
1
q
12.3km
=
1
q
0.48mG
12.3 km
Unknown:
=
E=?
0=?
=
1.00, or 0
=
=
=
2
1
r
1
q
8.99xl0
8.99x10
1.43 x 10—2 N/C
2
q
2.85 x lO_2 N/C
E
k
1
c
9
N
.m 2
C2
2
N
9
.m
=
(4.8X10 —4 C)
(l.74xl0
m
4
2
)
X
10
C
4
)
(1.23 x 10 4 m) 2
(4,8
45.0°
1. Calculate the magnitude of the electric
field strength produced by each
charge:
Because we are finding the magnitude of
the electric field strength, we can dis
regard the signs of each charge.
tan 0
The angle that r
2 makes with the coordinate system
equals the inverse tangent of
the ratio of the vertical to the horizonta
l components. Because these compone
nts
are equal,
The distance r
2 must be calculated from the information
in the diagram. Because r
2
forms the hypotenuse of a right triangle who
se sides equal r
, it follows that
1
= 2
J(rj) + (rj)
2 = .Jir
1 1.74 X i0 m
Given:
=
0.48 mC
1
r
The Seto-Ohashi bridge, linking the two Japa
nese islands of Honshu and
Shikoku, is the longest “rail and road” bridg
e, with an overall length of
12.3 km. Suppose two equal charges of 0.48
mC each are placed at the op
posite ends of the bridge. Find the electric
field strength, E, due to these
charges at the point exactly 12.3 km abov
e one of the bridge’s ends.
.ECTRIC FIELD STRENGTH
Ey,2
1
E
i_2
N/C
2 (cos 45.0°)
E
2.85 x
= (1.43 x iO N/C)(cos 45.0°)
1.01 X iO_2 N/C
= E
2 (sin 45.0°) = (1.43 X l0 N/C)(sin 45.0°)
=i.01
N
2
/C
x10
=
=
=
1.01
X 102
N/C
3.86 x l0_2 N/C
X
2
1
N
/C
0
N/C
75.3°
7. Evaluate your answer:
The electric field strergth has a magnitude of nearly 0.04 N/C
at the point
above the bridge. The vector’s net direction is to the right and
up from the
pOSiL)( axka
a.fl øf7S.3°
=
(3.86 x i02 N/C)
=3.82
(1.01 x 2
io
N
/C
6 = tan(3.82)
E()(
tan6—
10
E,
6. Use a suitable trigonometric function to find the direc
tion of the resultant
electric field strength vector:
ln this case, you can use the inverse tangent function.
X
/(L0l X l0 N/C
2) + (3.86 x 10-2 2
N/C)
=
=
f()2+ (E
2
)
0
=
5. Use the Pythagorean theorem to find the magnitude of the resul
tant
electric field strength vector:
=
0
tE
=Ey,i+Ey,2=t
2
1
/C
0
2.85X N
+ 1.01
=
Extot= E
1+E
= 0 + 1.01 X iO_2 N/C
2
4. Calculate the magnitude of the total electric field stren
gth in both the
x and y directions:
For E
:
2
1
For
:
E
unt.
q is positive.
slyLing
3, Find the xand y components of each electric field strength vecto
r:
At this point, the direction of each component must be taken into acco
The vector E
2 is directed at an angle upward and to the right because
The vector E
1 is directed vertically upward because q
1 is positive.
2. Determine the direction of each electric field strength vector I
the signs of the charges:
-
218 m
‘
2
1
q
1
5
0.Om
is the electric field strength at the center of the rectang
le? The value of
q is 6.4 nC.
5 The world’s largest windows, which are in the Palace
of Industry and
Technology in Paris, France, have a maximum width
of 218 m and a
maximum height of 50.0 m. Consider a rectangle with
these dimensions.
If charges are placed at its corners, as shown in the
figure below, what
the ground 120 m from the first charge, the horizontal
component of the
resultant electric field strength is found to be
E 1.60 x 102 N/C.
Using this information, calculate the unknown quantity
of charge.
3. Suppose three charges of 3.6 pC each are placed at
three corners of the
Imperial Palace in Beijing, China, which has a length of 960
m and a width
of 750 m,What is the strength of the electric field at the
fourth corner?
4. The largest fountain is found at Fountain Hills, Arizon
a. Under ideal
conditions, the 8000 kg column of water can reach as
high as 190 m.
Suppose a 12 nC charge is placed on the ground and anot
her charge of
unknown quantity is located 190 m above the first charge
. At a point on
The wheel held 10 first-class and 30 second-class cabins
, and each cabin
was capable of carrying 30 people. Consider two
cabins positioned
exactly opposite each other. Suppose one cabin has an
unbalanced charge
of 4.8 nC and the other cabin has a charge of 16 nC. At what
distance
from the 4.8 nC charge along the diameter of the wheel would
the
strength of the resultant electric field be zero?
2. In 1897, a Ferris wheel with a diameter of 86.5 m
was built in London.
1. Pontiac Silverdome Stadium, in Detroit, Michigan,
is the largest airsupported building in the world, with a length of 2.20 x 102
m and a
capacity to hold more than 80 000 people. If a charge of
18.0 pG is
placed at one end of the stadium and a charge of —12.0
pC is placed at
the other end of the stadium, what will be the strength
of the electric
field halfway between the charges?
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