1) Neutral hydrogen can be modeled as a positive point charge +1.6×10−19C surrounded by a distribution...
1) Neutral hydrogen can be modeled as a positive point charge
+1.6×10−19C surrounded by a distribution of negative
charge with volume density given by
ρE(r)=−Ae−2r/a0 where
a0=0.53×10−10m is called the Bohr
radius, A is a constant such that the total amount of negative
charge is −1.6×10−19C, and e = 2.718... is the base of
the natural log.
[Hint: Do not confuse the exponential number e with the
elementary charge e which uses the same symbol but has a completely
different meaning and value (e=1.6×10−19C).
a) What is the net charge inside a sphere of radius a0?
b) What is the strength of the electric field at a distance a0 from the nucleus?
2) A point charge of 9.40 nC is located at the origin and a second charge of -4.20 nC is located on the x axis at x=3.75cm.
a) Calculate the electric flux through a sphere centered at the origin with radius 1.20 m .
b) Repeat the calculation for a sphere of radius 2.70 m .
Homework Answers
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1) Neutral hydrogen can be modeled as a positive point charge
+1.6×10−19C surrounded by a distribution...
A hydrogen atom consists of a proton, effectively a point charge of +1.6 × 10^-19C, surrounded...
A hydrogen atom consists of a proton, effectively a point charge of +1.6 × 10^-19C, surrounded by a spherical “electron cloud” of radius 5.3 × 10^-11m and charge −1.6 × 10^-19C. Use Gauss’s Law to find the electric field at a point (a) 2 × 10^-11m from the proton (inside the atom) and (b) 1 × 10^-10m from the proton (outside).
1) A point charge of 9.40 nC is located at the origin and a second charge...
1) A point charge of 9.40 nC is located at the origin and a
second charge of -4.20 nC is located on the x axis at x=3.75cm.
a) Calculate the electric flux through a sphere centered at the
origin with radius 1.20 m .
b) Repeat the calculation for a sphere of radius 2.70 m .
2) In a cubical volume, 0.70 m on a side, the electric field
is
where E0=0.125N/C and a=0.70m. The cube has its sides
parallel...
Why the E field due to point charge need to be negative? Positive charge is distributed...
Why the E field due to point charge need to be negative?
Positive charge is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A particle with a positive charge is placed at x = 2R on the x axis. The magnitude of the electric field at x = R/2 on the x axis is: (62) 89 (A) 4NER2 QC) E ye B + 478, RP - 727€R? 81ER2 70 due to point) 1878 R2 charge...
Equipotential surfaces A positive point charge is surrounded by an equipotential surface A, which has a...
Equipotential surfaces A positive point charge is surrounded by an equipotential surface A, which has a radius of rA. A positive test charge moves from surface A to another equipotential surface B, which has a radius rB. In the process, the electric force does negative work (a) Does the electric force acting on the test charge have the same or opposite direction as the displacement of the test charge? O The electric force has the same direction as the displacement...
BONUS: Electron Cloud In the Bohr model of hydrogen, the electron is treated as a point...
BONUS: Electron Cloud In the Bohr model of hydrogen, the electron is treated as a point particle orbiting the nucleus at a distance of Og . 5.3. 10-11 m Reality is not so simple, however. The charge of the electron is distributed around the nucleus in a spherically symmetrie, nonuniform manner. (ais merely the most probable distance between the electron and the nucleus.) In this problem, we will explore the electric fields within a hydrogen atom using Gauss' law. Treat...
all T-Mobile 10:52 PM Done 1 of 7 PHYS 2212: Gauss Law Group Worlk Problem #...
all T-Mobile 10:52 PM Done 1 of 7 PHYS 2212: Gauss Law Group Worlk Problem # 2 Instructions: This is a fundamental problem that can be solved using Gauss' Law. In your group. discuss the problem and work out the solution. Prepare to present that solution on the board during the next class. Hand in your solution on paper for credit. 1 A neutral hydrogen atom in its normal state behaves like an electric charge distribution that consists of a...
(3) A point charge of 10 nC sits at the origin. [5 pts] (a) Sketch the...
(3) A point charge of 10 nC sits at the origin. [5 pts] (a) Sketch the point charge and it electric field lines. (b) Now sketch a spherical surface of radius 2 m that sits on the x-axis at x-4m. Assume there is no charge on the spherical surface. (Sketch in 2D i.e. include just the projection of the sphere on the x-y plane.) (c) How many of your drawn lines enter the spherical surface? (d) How many lines leave...
2. In the derivation of the energy levels in the hydrogen atom one commonly assumes that the nucleus is a point charge. However, in reality the size of the nucleus is of the order of Im = 10-15m. Sin...
2. In the derivation of the energy levels in the hydrogen atom one commonly assumes that the nucleus is a point charge. However, in reality the size of the nucleus is of the order of Im = 10-15m. Since this is very much smaller than the typical distance of the electron from the nucleus, which is of the order of a0-0.5A = 0.5 × 10-10m, the finite size of the nucleus can be taken into account perturbatively. (a) Assume that...
Question 1 (compulsory): The following set of charges is given in free space Charge σ,--40 nC/m Number and type of charge #1 , charged spherical shell of radius Ri-10 cm carrying uniform surface char...
Question 1 (compulsory): The following set of charges is given in free space Charge σ,--40 nC/m Number and type of charge #1 , charged spherical shell of radius Ri-10 cm carrying uniform surface charge density σ #2, charged spherical shell of radius R2-5 cm carrying uniform surface charge density Ơ Location (0, 0, 0) m (position of the centre of the sphere) (0, 0, 0) m (position of the centre of the sphere σ,-160 nC/m2 The positions of the spheres'...
1. An infinite line of uniform positive charge runs along the x axis and has a...
1. An infinite line of uniform positive charge runs along the x axis and has a line charge density of λ=20.8 m nC . Consider the point (0 m, 2.00 m) which is located 2.00 meters above the infinite line. What is the magnitude of the electric field at this point? 2. An infinite horizontal plane of uniform negative charge sits at a height ofz=0. For a point at a height of z=−3m (i.e., 3 meters below the infinite plane),...
1) A point charge of 9.40 nC is located at the origin and a
second charge of -4.20 nC is located on the x axis at x=3.75cm.
a) Calculate the electric flux through a sphere centered at the
origin with radius 1.20 m .
b) Repeat the calculation for a sphere of radius 2.70 m .
2) In a cubical volume, 0.70 m on a side, the electric field
is
where E0=0.125N/C and a=0.70m. The cube has its sides
parallel...
Why the E field due to point charge need to be negative?
Positive charge is distributed uniformly throughout an insulating sphere of radius R, centered at the origin. A particle with a positive charge is placed at x = 2R on the x axis. The magnitude of the electric field at x = R/2 on the x axis is: (62) 89 (A) 4NER2 QC) E ye B + 478, RP - 727€R? 81ER2 70 due to point) 1878 R2 charge...
Equipotential surfaces A positive point charge is surrounded by an equipotential surface A, which has a radius of rA. A positive test charge moves from surface A to another equipotential surface B, which has a radius rB. In the process, the electric force does negative work (a) Does the electric force acting on the test charge have the same or opposite direction as the displacement of the test charge? O The electric force has the same direction as the displacement...
BONUS: Electron Cloud In the Bohr model of hydrogen, the electron is treated as a point particle orbiting the nucleus at a distance of Og . 5.3. 10-11 m Reality is not so simple, however. The charge of the electron is distributed around the nucleus in a spherically symmetrie, nonuniform manner. (ais merely the most probable distance between the electron and the nucleus.) In this problem, we will explore the electric fields within a hydrogen atom using Gauss' law. Treat...
all T-Mobile 10:52 PM Done 1 of 7 PHYS 2212: Gauss Law Group Worlk Problem # 2 Instructions: This is a fundamental problem that can be solved using Gauss' Law. In your group. discuss the problem and work out the solution. Prepare to present that solution on the board during the next class. Hand in your solution on paper for credit. 1 A neutral hydrogen atom in its normal state behaves like an electric charge distribution that consists of a...
(3) A point charge of 10 nC sits at the origin. [5 pts] (a) Sketch the point charge and it electric field lines. (b) Now sketch a spherical surface of radius 2 m that sits on the x-axis at x-4m. Assume there is no charge on the spherical surface. (Sketch in 2D i.e. include just the projection of the sphere on the x-y plane.) (c) How many of your drawn lines enter the spherical surface? (d) How many lines leave...
2. In the derivation of the energy levels in the hydrogen atom one commonly assumes that the nucleus is a point charge. However, in reality the size of the nucleus is of the order of Im = 10-15m. Since this is very much smaller than the typical distance of the electron from the nucleus, which is of the order of a0-0.5A = 0.5 × 10-10m, the finite size of the nucleus can be taken into account perturbatively. (a) Assume that...
Question 1 (compulsory): The following set of charges is given in free space Charge σ,--40 nC/m Number and type of charge #1 , charged spherical shell of radius Ri-10 cm carrying uniform surface charge density σ #2, charged spherical shell of radius R2-5 cm carrying uniform surface charge density Ơ Location (0, 0, 0) m (position of the centre of the sphere) (0, 0, 0) m (position of the centre of the sphere σ,-160 nC/m2 The positions of the spheres'...
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