CALC A Nonuniformly Charged Slab. Repeat Problem 22.54, but now let the charge density of the slab be given by ρ ( x ) = ρ 0 ( x / d ) 2 , where ρ 0 is a positive constant. 22.54 A Uniformly Charged Slab. A slab of insulating material has thickness 2 d and is oriented so that its faces are parallel to the yz -plane and given by the planes x = d and x = − d . The y - and z -dimensions of the slab are very large compared to d ; treat (hem as essentially infinite. The slab has a uniform positive charge density ρ . (a) Explain why the electric field due to the slab is zero at the center of the slab ( x = 0). (b) Using Gauss’s law, find the electric field due to the slab (magnitude and direction) at all points in space.
CALC A Nonuniformly Charged Slab. Repeat Problem 22.54, but now let the charge density of the slab be given by ρ ( x ) = ρ 0 ( x / d ) 2 , where ρ 0 is a positive constant. 22.54 A Uniformly Charged Slab. A slab of insulating material has thickness 2 d and is oriented so that its faces are parallel to the yz -plane and given by the planes x = d and x = − d . The y - and z -dimensions of the slab are very large compared to d ; treat (hem as essentially infinite. The slab has a uniform positive charge density ρ . (a) Explain why the electric field due to the slab is zero at the center of the slab ( x = 0). (b) Using Gauss’s law, find the electric field due to the slab (magnitude and direction) at all points in space.
CALC A Nonuniformly Charged Slab. Repeat Problem 22.54, but now let the charge density of the slab be given by ρ(x) = ρ0(x/d)2, where ρ0 is a positive constant.
22.54 A Uniformly Charged Slab. A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x = d and x = −d. The y- and z-dimensions of the slab are very large compared to d; treat (hem as essentially infinite. The slab has a uniform positive charge density ρ. (a) Explain why the electric field due to the slab is zero at the center of the slab (x = 0). (b) Using Gauss’s law, find the electric field due to the slab (magnitude and direction) at all points in space.
Fresnel lens: You would like to design a 25 mm diameter blazed Fresnel zone plate with a first-order power of
+1.5 diopters. What is the lithography requirement (resolution required) for making this lens that is designed
for 550 nm? Express your answer in units of μm to one decimal point.
Fresnel lens: What would the power of the first diffracted order of this lens be at wavelength of 400 nm?
Express your answer in diopters to one decimal point.
Eye: A person with myopic eyes has a far point of 15 cm. What power contact lenses does she need to correct
her version to a standard far point at infinity? Give your answer in diopter to one decimal point.
Paraxial design of a field flattener. Imagine your optical system has Petzal curvature of the field with radius
p. In Module 1 of Course 1, a homework problem asked you to derive the paraxial focus shift along the axis
when a slab of glass was inserted in a converging cone of rays. Find or re-derive that result, then use it to
calculate the paraxial radius of curvature of a field flattener of refractive index n that will correct the observed
Petzval. Assume that the side of the flattener facing the image plane is plano. What is the required radius of
the plano-convex field flattener? (p written as rho )
3.37(a) Five free electrons exist in a three-dimensional infinite potential well with all three widths equal to \( a = 12 \, \text{Å} \). Determine the Fermi energy level at \( T = 0 \, \text{K} \). (b) Repeat part (a) for 13 electrons.
Book: Semiconductor Physics and Devices 4th ed, NeamanChapter-3Please expert answer only. don't give gpt-generated answers, & please clear the concept of quantum states for determining nx, ny, nz to determine E, as I don't have much idea about that topic.
Chapter 22 Solutions
University Physics with Modern Physics (14th Edition)
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