CP CALC A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density ρ ( r ) is given by ρ ( r ) = 3 αr / 2 R f o r r ≤ R / 2 ρ ( r ) = α [ 1 − ( r / R ) 2 ] f o r R / 2 ≤ r ≤ R ρ ( r ) = 0 f o r r ≥ R Here α is a positive constant having units of C/m 3 , (a) Determine α in terms of Q and R . (b) Using Gauss’s law, derive an expression for the magnitude of the electric field as a function of r . Do this separately for all three regions. Express your answers in terms of Q . (c) What fraction of the total charge is contained within the region R /2 ≤ r ≤ R ? (d) What is the magnitude of E → at r = R /2? (e) If an electron with charge q ' = − e is released from rest at any point in any of the three regions, the resulting motion will be oscillatory but not simple harmonic. Why?
CP CALC A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density ρ ( r ) is given by ρ ( r ) = 3 αr / 2 R f o r r ≤ R / 2 ρ ( r ) = α [ 1 − ( r / R ) 2 ] f o r R / 2 ≤ r ≤ R ρ ( r ) = 0 f o r r ≥ R Here α is a positive constant having units of C/m 3 , (a) Determine α in terms of Q and R . (b) Using Gauss’s law, derive an expression for the magnitude of the electric field as a function of r . Do this separately for all three regions. Express your answers in terms of Q . (c) What fraction of the total charge is contained within the region R /2 ≤ r ≤ R ? (d) What is the magnitude of E → at r = R /2? (e) If an electron with charge q ' = − e is released from rest at any point in any of the three regions, the resulting motion will be oscillatory but not simple harmonic. Why?
CP CALC A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density ρ(r) is given by
ρ
(
r
)
=
3
αr
/
2
R
f
o
r
r
≤
R
/
2
ρ
(
r
)
=
α
[
1
−
(
r
/
R
)
2
]
f
o
r
R
/
2
≤
r
≤
R
ρ
(
r
)
=
0
f
o
r
r
≥
R
Here α is a positive constant having units of C/m3, (a) Determine α in terms of Q and R. (b) Using Gauss’s law, derive an expression for the magnitude of the electric field as a function of r. Do this separately for all three regions. Express your answers in terms of Q. (c) What fraction of the total charge is contained within the region R/2 ≤ r ≤ R? (d) What is the magnitude of
E
→
at r = R/2? (e) If an electron with charge q' = −e is released from rest at any point in any of the three regions, the resulting motion will be oscillatory but not simple harmonic. Why?
Imagine you are out for a stroll on a sunny day when you encounter a lake. Unpolarized light from the sun is reflected off the lake into your eyes. However, you notice when you put on your vertically polarized sunglasses, the light reflected off the lake no longer reaches your eyes. What is the angle between the unpolarized light and the surface of the water, in degrees, measured from the horizontal? You may assume the index of refraction of air is nair=1 and the index of refraction of water is nwater=1.33 . Round your answer to three significant figures. Just enter the number, nothing else.
Chapter 22 Solutions
University Physics, Volume 2 - Technology Update Custom Edition for Texas A&M - College Station, 2/e
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