(III) The dipole moment, considered as a vector, points from the negative to the positive charge. The water molecule, Fig. 23–32, has a dipole moment p → which can be considered as the vector sum of the two dipole moments p → 1 and p → 2 as shown. The distance between each H and the O is about 0.96 × 10 −10 m; the lines joining the center of the O atom with each H atom make an angle or 104° as shown, and the net dipole moment has been measured to be p = 6.1 × 10 −30 C · m. ( a ) Determine the effective charge q on each H atom. ( b ) Determine the electric potential, far from the molecule, due to each dipole, p → 1 and p → 2 , and show that V = 1 4 π ϵ 0 p cos θ r 2 where p is the magnitude or the net dipole moment, p → = p → 1 + p → 2 , and V is the total potential due to both p → 1 and p → 2 . Take V = 0 at r = ∞. FIGURE 23–32 Problem 46.
(III) The dipole moment, considered as a vector, points from the negative to the positive charge. The water molecule, Fig. 23–32, has a dipole moment p → which can be considered as the vector sum of the two dipole moments p → 1 and p → 2 as shown. The distance between each H and the O is about 0.96 × 10 −10 m; the lines joining the center of the O atom with each H atom make an angle or 104° as shown, and the net dipole moment has been measured to be p = 6.1 × 10 −30 C · m. ( a ) Determine the effective charge q on each H atom. ( b ) Determine the electric potential, far from the molecule, due to each dipole, p → 1 and p → 2 , and show that V = 1 4 π ϵ 0 p cos θ r 2 where p is the magnitude or the net dipole moment, p → = p → 1 + p → 2 , and V is the total potential due to both p → 1 and p → 2 . Take V = 0 at r = ∞. FIGURE 23–32 Problem 46.
(III) The dipole moment, considered as a vector, points from the negative to the positive charge. The water molecule, Fig. 23–32, has a dipole moment
p
→
which can be considered as the vector sum of the two dipole moments
p
→
1
and
p
→
2
as shown. The distance between each H and the O is about 0.96 × 10−10 m; the lines joining the center of the O atom with each H atom make an angle or 104° as shown, and the net dipole moment has been measured to be p = 6.1 × 10−30C · m. (a) Determine the effective charge q on each H atom. (b) Determine the electric potential, far from the molecule, due to each dipole,
p
→
1
and
p
→
2
, and show that
V
=
1
4
π
ϵ
0
p
cos
θ
r
2
where p is the magnitude or the net dipole moment,
p
→
=
p
→
1
+
p
→
2
, and V is the total potential due to both
p
→
1
and
p
→
2
. Take V = 0 at r = ∞.
How many excess electrons must be placed on each of two small spheres spaced 3cm apart if the speheres are to have equal charge and if the force of repulsion between them is to be 10^-19N?
The magnitude of the electric fie ld at a distance r from a point charge O is equal to O/4πεor2. How close to a water molecule (of polarizability volume 1.48 x 1-30 m3) must a proton approach before the dipole moment it induces is equal to the permanent dipole moment of the molecule (1.85 D)?
A dipole with dipole-moment 17.0 mC-m is initially oriented in the positive y-axis. How much work is required to rotate the dipole until it is oriented along the x-axis if the dipole is in an electric field with strength 87.0 kN/C (in positive x-direction)?
Chapter 23 Solutions
Physics For Scientists & Engineers With Modern Physics, Vol. 3 (chs 36-44) (4th Edition)
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