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3. Gauss' Lau: Weather balloons are typically filled with hydrogen and reach a diameter of 8...
Question 1 (compulsory): (i) State Gauss' law for the electric field (E-field) in words and explain its meaning. Write the corresponding mathematical expression and clearly define all symbols...
Question 1 (compulsory): (i) State Gauss' law for the electric field (E-field) in words and explain its meaning. Write the corresponding mathematical expression and clearly define all symbols and operations used. Describe one application of Gauss' law. 15% (ii) A very long wire carrying electric charge with uniform line charge density is located in free space. Applying Gauss' law, derive the E-field due to this wire. Clearly explain every step of your derivation and the assumptions you take. 40% Find...
3. For a while in the early 20th century one proposed model for the structure of...
3. For a while in the early 20th century one proposed model for the structure of atoms was that a positive point charge (the nucleus) +Ze was at the center of a charged sphere of radius R and charge -Ze. To be clear, the negative charge in the sphere was proposed to be spread through the volume of the sphere, not on its surface. Z is the atomic number. (a) In terms of the symbols, Z and R, what is...
We'll work througil uhe caitul 3. In this problem, of the electric field near the surface of a la...
we'll work througil uhe caitul 3. In this problem, of the electric field near the surface of a large, flat metal conductor. In the image at right, the square represents a section of the conductor's surface. The region above the surface is empty space, and below the surface is solid conducting metal. There is a uniform positive surface charge density +σ on the surface of the conductor. R I What is the electric field inside the conductor? Explain your reasoning....
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...
1. Explain the variational principle and illustrate it with some example (different from the one in...
1. Explain the variational principle and illustrate it with some example (different from the one in the following point) 2. A trial function for ls electron in hydrogen atom has a form of (r) = e-ara. Derive the nor- malization constant. Explain the difference between this trial function and the true l-electron hydrogen-like orbital. 3. The expression for energy as a function of a for the H-atom using above trial function is given by: E(a) = 3h2a 2me e2a1/2 21/26073/2...
L(a) A long (L>> a) cylinder in vacuum has a line charge density p is shown...
L(a) A long (L>> a) cylinder in vacuum has a line charge density p is shown below, (). State the Gauss's law for electric field in words. [1) (i). In order to calculate the electric field inside the cylinder using Gauss's Law, draw an appropriate Gaussian surface in the cylinder. [1] (i). Use the above information or otherwise, show that the electric field in the radial direction Pt inside the cylinder is ,2a (assume that the charge is evenly distributed...
answer both please 3. (10 pts.) One often forgets the curl has a physical meaning. The...
answer both please
3. (10 pts.) One often forgets the curl has a physical meaning. The curl operator differs from the divergence field to produce another field. Since vectors are more operator in that it acts on a_ complicated than scalars it is important to understand the purpose of the curl operator. Let E (r.y, :) be some electric field. The mathematical expression for the curl of is written as ex ey e .az _ ax)s+(a --dy)互 az广ㄨ oy The...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
3 Casimir effect c. All vacuum energies considered so far are infinite. In reality, the metal wal...
3 Casimir effect c. All vacuum energies considered so far are infinite. In reality, the metal walls are conduc tors only at finite frequencies, and thus do not impose boundary conditions at infinite frqu cies. (The cutoff is given roughly by the plasma frequencywp Thus, we need (and should) not consider infinite frequencies in our equations. To remove We will derive the Casimir effect in thee d sions, making use of the Euler-Maclaurin formula imen- them, we introduce a cutoff...
5:16 lLTE ) Done 1 of 5 Assessment #1 (Kinematics of a Particle) Rectilinear Motion (Straight...
5:16 lLTE ) Done 1 of 5 Assessment #1 (Kinematics of a Particle) Rectilinear Motion (Straight linc Motion 3. The position of a point during the interval of time from r otor 6 is given by ** * m. (a) What is the maximum velocity during this interval of time, and at what time does it occur? (b) What is the acceleration when the velocity is a maximum? (20 m/s, 0 m/s 3. A test projectile is fired horizontally into...
Question 1 (compulsory): (i) State Gauss' law for the electric field (E-field) in words and explain its meaning. Write the corresponding mathematical expression and clearly define all symbols and operations used. Describe one application of Gauss' law. 15% (ii) A very long wire carrying electric charge with uniform line charge density is located in free space. Applying Gauss' law, derive the E-field due to this wire. Clearly explain every step of your derivation and the assumptions you take. 40% Find...
3. For a while in the early 20th century one proposed model for the structure of atoms was that a positive point charge (the nucleus) +Ze was at the center of a charged sphere of radius R and charge -Ze. To be clear, the negative charge in the sphere was proposed to be spread through the volume of the sphere, not on its surface. Z is the atomic number. (a) In terms of the symbols, Z and R, what is...
we'll work througil uhe caitul 3. In this problem, of the electric field near the surface of a large, flat metal conductor. In the image at right, the square represents a section of the conductor's surface. The region above the surface is empty space, and below the surface is solid conducting metal. There is a uniform positive surface charge density +σ on the surface of the conductor. R I What is the electric field inside the conductor? Explain your reasoning....
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...
1. Explain the variational principle and illustrate it with some example (different from the one in the following point) 2. A trial function for ls electron in hydrogen atom has a form of (r) = e-ara. Derive the nor- malization constant. Explain the difference between this trial function and the true l-electron hydrogen-like orbital. 3. The expression for energy as a function of a for the H-atom using above trial function is given by: E(a) = 3h2a 2me e2a1/2 21/26073/2...
L(a) A long (L>> a) cylinder in vacuum has a line charge density p is shown below, (). State the Gauss's law for electric field in words. [1) (i). In order to calculate the electric field inside the cylinder using Gauss's Law, draw an appropriate Gaussian surface in the cylinder. [1] (i). Use the above information or otherwise, show that the electric field in the radial direction Pt inside the cylinder is ,2a (assume that the charge is evenly distributed...
answer both please
3. (10 pts.) One often forgets the curl has a physical meaning. The curl operator differs from the divergence field to produce another field. Since vectors are more operator in that it acts on a_ complicated than scalars it is important to understand the purpose of the curl operator. Let E (r.y, :) be some electric field. The mathematical expression for the curl of is written as ex ey e .az _ ax)s+(a --dy)互 az广ㄨ oy The...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
3 Casimir effect c. All vacuum energies considered so far are infinite. In reality, the metal walls are conduc tors only at finite frequencies, and thus do not impose boundary conditions at infinite frqu cies. (The cutoff is given roughly by the plasma frequencywp Thus, we need (and should) not consider infinite frequencies in our equations. To remove We will derive the Casimir effect in thee d sions, making use of the Euler-Maclaurin formula imen- them, we introduce a cutoff...
5:16 lLTE ) Done 1 of 5 Assessment #1 (Kinematics of a Particle) Rectilinear Motion (Straight linc Motion 3. The position of a point during the interval of time from r otor 6 is given by ** * m. (a) What is the maximum velocity during this interval of time, and at what time does it occur? (b) What is the acceleration when the velocity is a maximum? (20 m/s, 0 m/s 3. A test projectile is fired horizontally into...
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