The charge density
ρ ( r → ) for a single water molecule oriented in the z=0 plane
with one hydrogen at the origin, the oxygen at (77,59,0), and the
second hydrogen at (153,0,0) can be approximated as:
in units of picometers for length and elementary charge for charge.
How much charge is on the first hydrogen at the origin?
Homework Answers
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The charge density
ρ ( r → ) for a single water molecule oriented in the...
2. The charge distribution of a water molecule can be approximated by the diagram shown. The...
2. The charge distribution of a water molecule can be approximated by the diagram shown. The + charges represent the hydrogen atoms, cach distance from the origin, and the -2 charge represents the oxygen atom, located a distance b from the origin a. (8 pts.) Find an expression for the electric potential at the pointy, located on the y-axis, as shown. Assume that the potential is zero at a distance of infinity from the molecule + to b. (12 pts.)...
Imagine that a water molecule is made of two positively charged hydrogen atoms, each with charge...
Imagine that a water molecule is made of two positively charged
hydrogen atoms, each with charge +q, and one negatively charged
oxygen atom, with charge –2q. These atoms are arranged as shown.
The magnitude of the electron charge q = 1.6 x 10^19 C and the
distance unit used in the diagram, “pm”, is picometers, or 10^-12
m. How much energy would it take for you to completely remove the
positively charged hydrogen atom on the left from this molecule,...
1) Water is a polar molecule. There is an effective accumulation of negative charge near the...
1) Water is a polar molecule. There is an effective accumulation of negative charge near the oxygen atom and an effective lack of negative charge ( positive charge) near each of the hydrogen atoms. The molecule is triangular in shape, as diagramed below, with the angle near the oxygen vertex equal to 104.5°. d is the distance from each of the hydrogen atoms to the oxygen atom +Q 5225 52.25 -20 +Q Derive a formula for the electric field produced...
A long, cylindrical wire with a radius of R carries a charge density of ρ =...
A long, cylindrical wire with a radius of R carries a charge density of ρ = ks^2. Find the electric field inside and outside of the wire. This questions is theory based
If R is a solid in space with density ρ(x, y, z), it's centre of mass...
If R is a solid in space with density ρ(x, y, z), it's centre of mass is the point with coordinates i, y, 2, given by za(x, y, z) dV, where z, y, z) dV is the mass of the object. Find the centre of mass of each solid R below (a) Rls the cube with 0 < x < b, 0· у<b, 0-2-band ρ(x, y, z) = x2 + y2 + 22; (b) R is the tetrahedron bounded by...
Consider an infinite slab of thickness 2a and uniform volume charge density ρ. This is essentially...
Consider an infinite slab of thickness 2a and uniform volume charge density ρ. This is essentially an infinite plane with a non-negligible thickness. Since the planar symmetry involves:艹-2 reflection symmetry, as well as the translation symmetry along the and y direc- tions, we place the origin at a point on the midplane of the slab. In other words, the midplane corresponds to oo = 0 (i.e., the ry plane) and the surfaces of the slab are at a (a) Use...
4.1 A sphere of radius R has a uniform volume charge density ρ(r) Pr. A. Calculate...
4.1 A sphere of radius R has a uniform volume charge density ρ(r) Pr. A. Calculate E(r) B. Use your answer to A to calculate V(r). C. Use your answer to B to calculate the energy of this charge configuration, via the expression U pV d where the integral must be evaluated over the bounded charge distribution. D. Use your answer to A to calculate the energy of this charge configuration, via the expression 2 2 space
A solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 ,...
A solid insulating sphere of radius R has a non-uniform charge density ρ = Ar2 , where A is a constant and r is measured from the center of the sphere. a) Show that the electric field outside the sphere (r > R) is E = AR5 /(5εor 2 ). b) Show that the electric field inside the sphere (r < R) is E = AR3 /(5εo). Hint: The total charge Q on the sphere is found by integrating ρ...
In a container with a circular base (R = 0.2 m) water (density ρ = 997...
In a container with a circular base (R = 0.2 m) water (density ρ = 997 filled up to a height h 0.5m Hint:Assume a frictionless fluid. Note that R. ) is Im Figure 2: water container a) At which height from the bottom of the container an opening should be put so that the water hits the ground at the furthest distance from the jar? (2P) b) Now the opening (circular, r0.5 ) is put at y 0.3m. Calculate...
In free space, consider the volume charge density ρ,-100 μCm3 present throughout the region 5 mm<r<10...
In free space, consider the volume charge density ρ,-100 μCm3 present throughout the region 5 mm<r<10 mm and pv-0 for 0<r<5 mm. (a) Find the total charge inside the spherical surfacer 10 mm. in spherical coordinates (b) Find D, at r = 10 mm, Dr(10mm) = 2 (c) If there is no charge for r >10 mm, find D, at-50 mm Dr (50 mm)-- 2 47(r)2
2. The charge distribution of a water molecule can be approximated by the diagram shown. The + charges represent the hydrogen atoms, cach distance from the origin, and the -2 charge represents the oxygen atom, located a distance b from the origin a. (8 pts.) Find an expression for the electric potential at the pointy, located on the y-axis, as shown. Assume that the potential is zero at a distance of infinity from the molecule + to b. (12 pts.)...
Imagine that a water molecule is made of two positively charged
hydrogen atoms, each with charge +q, and one negatively charged
oxygen atom, with charge –2q. These atoms are arranged as shown.
The magnitude of the electron charge q = 1.6 x 10^19 C and the
distance unit used in the diagram, “pm”, is picometers, or 10^-12
m. How much energy would it take for you to completely remove the
positively charged hydrogen atom on the left from this molecule,...
1) Water is a polar molecule. There is an effective accumulation of negative charge near the oxygen atom and an effective lack of negative charge ( positive charge) near each of the hydrogen atoms. The molecule is triangular in shape, as diagramed below, with the angle near the oxygen vertex equal to 104.5°. d is the distance from each of the hydrogen atoms to the oxygen atom +Q 5225 52.25 -20 +Q Derive a formula for the electric field produced...
If R is a solid in space with density ρ(x, y, z), it's centre of mass is the point with coordinates i, y, 2, given by za(x, y, z) dV, where z, y, z) dV is the mass of the object. Find the centre of mass of each solid R below (a) Rls the cube with 0 < x < b, 0· у<b, 0-2-band ρ(x, y, z) = x2 + y2 + 22; (b) R is the tetrahedron bounded by...
Consider an infinite slab of thickness 2a and uniform volume charge density ρ. This is essentially an infinite plane with a non-negligible thickness. Since the planar symmetry involves:艹-2 reflection symmetry, as well as the translation symmetry along the and y direc- tions, we place the origin at a point on the midplane of the slab. In other words, the midplane corresponds to oo = 0 (i.e., the ry plane) and the surfaces of the slab are at a (a) Use...
4.1 A sphere of radius R has a uniform volume charge density ρ(r) Pr. A. Calculate E(r) B. Use your answer to A to calculate V(r). C. Use your answer to B to calculate the energy of this charge configuration, via the expression U pV d where the integral must be evaluated over the bounded charge distribution. D. Use your answer to A to calculate the energy of this charge configuration, via the expression 2 2 space
In a container with a circular base (R = 0.2 m) water (density ρ = 997 filled up to a height h 0.5m Hint:Assume a frictionless fluid. Note that R. ) is Im Figure 2: water container a) At which height from the bottom of the container an opening should be put so that the water hits the ground at the furthest distance from the jar? (2P) b) Now the opening (circular, r0.5 ) is put at y 0.3m. Calculate...
In free space, consider the volume charge density ρ,-100 μCm3 present throughout the region 5 mm<r<10 mm and pv-0 for 0<r<5 mm. (a) Find the total charge inside the spherical surfacer 10 mm. in spherical coordinates (b) Find D, at r = 10 mm, Dr(10mm) = 2 (c) If there is no charge for r >10 mm, find D, at-50 mm Dr (50 mm)-- 2 47(r)2
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