2nd exam, 2007.
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-- psigy - 2008.01.13.
Tartalomjegyzék
- 1 I. Problems (2 points each):
- 1.1 1. A current of 10A is flowing in a clockwise direction in a circular loop having a radius a = 2cm. Another current of 10A is flowing in the opposite direction in another, concentric circular loop having a radius b = 4.5cm. Find the magnetic field at the center.
- 1.2 2. A long, straight wire carries a current of 10A. At a distance of 1cm from the wire a point charge of 100nC is moving perpendicularly to the wire with 106 m/s instantaneous speed. Find the Lorentz-force acting on the point charge at this point.
- 1.3 3. A current of 2A flows in a cylindrical wire having a radius of 1mm. How far from the axis of the wire (outside the wire) does the magnetic field have the same value as at a distance 0.5mm from the axis?
- 1.4 4. Find the magnetic energy stored in a toroid whose central line is 1m long, the cross sectional area is 10cm2 and the current is 2A. The toroid has 1000 turns.
- 1.5 5. 10 turns of wire are tightly wound around a solenoid having a length of 12.56cm and a cross-sectional area of 5cm2. The number of turns of the solenoid is 200. Find the mutual inductance.
- 1.6 6. Two slits at a distance of 0.4mm from each other are illuminated with blue light (=400nm). Find the distance between the interference fringes if the screen is 1 meter away from the slits.
- 1.7 7. Calculate the ratio between (1) the power incident on a 4mm2 surface at a distance 1 meter from a 25W light bulb, and (2) the power incident on the same surface if it is illuminated by a 1mW laser. The diameter of the laser beam is 1mm.
- 1.8 8. An electron is confined to a 1D box in which its ground state energy is 2eV. How much energy is required to excite the electron into the next energy state?
- 1.9 9. Determine the number of electrons that can occupy the n=3 shell in an atom.
- 1.10 10. Find the smallest possible value of the angle between the orbital angular momentum vector and an external magnetic field for an electron in a 3d state of hydrogen.
- 2 II. True-false statements (1 point each):
- 2.1 1. According to Biot-Savart's law the magnetic field is inversely proportional to the cube of the distance from the current element.
- 2.2 2. The flux of for a closed surface is always zero.
- 2.3 3. The Hall-effect can be a useful tool for measuring the magnetic field.
- 2.4 4. If the net current across a surface bounded by a closed loop is zero, then the magnetic field is zero everywhere along the loop.
- 2.5 5. Paramagnetic materials cannot be gases or liquids.
- 2.6 6. The line integral of the magnetic field strength can be measured in W/V.
- 2.7 7. The mutual inductance depends on the applied current.
- 2.8 8. In Young's double slit experiment, when the illumination is white light, the zeroth-order fringe is in color.
- 2.9 9. When an incident light of any polarization comes at Brewster's angle, there is no reflection.
- 2.10 10. The resolution of an astronomical telescope is independent of the observed wavelength.
- 2.11 11. In blackbody radiation, the total emitted power is proportional to the fourth power of the temperature.
- 2.12 12. In blackbody radiation, the temperature multiplied by the maximal wavelength gives a universal constant.
- 2.13 13. Natural line broadening in a laser can be explained using Heisenberg's uncertainty principle.
- 2.14 14. Covalent bond is caused by the Coulomb attraction between two ions.
- 2.15 15. Knowing the rotational energy levels of a molecule gives us information about the bond strength.
- 3 III. Theory (3 points each):
- 3.1 1. What interpretational difficulties arise in relation with the magnetic permeability of ferromagnetic materials?
- 3.2 2. How can we produce linearly polarized light out of unpolarized light? (List at least 2 or 3 different methods.)
- 3.3 3. Why are at least 3 energy levels necessary in optical laser pumping?
- 3.4 4. What is Wien’s displacement law of blackbody radiation?
- 3.5 5. What is the physical meaning of the square of the absolute value of the wave function?
I. Problems (2 points each):
1. A current of 10A is flowing in a clockwise direction in a circular loop having a radius a = 2cm. Another current of 10A is flowing in the opposite direction in another, concentric circular loop having a radius b = 4.5cm. Find the magnetic field at the center.
(a) 174T (b) 235T (c) 450T (d) none
[math]\sum B= |B_1 -B_2|[/math]
[math] B_1= \frac {\mu_0*I_1}{2*r_1} = 1,3962*10^{-4} [/math]
[math] B_2= \frac {\mu_0*I_2}{2*r_2} = 3,141*10^{-4} [/math]
[math] B_2-B_1 = 1,74*10^{-4} [/math]
- a*
2. A long, straight wire carries a current of 10A. At a distance of 1cm from the wire a point charge of 100nC is moving perpendicularly to the wire with 106 m/s instantaneous speed. Find the Lorentz-force acting on the point charge at this point.
(a) 0.02mN (b) 0.1mN (c) 1.65mN (d) none
[math]\ B= \frac {\mu_0*I}{2*\pi*R} [/math]
[math]F= Q*v*B[/math]
- a*
3. A current of 2A flows in a cylindrical wire having a radius of 1mm. How far from the axis of the wire (outside the wire) does the magnetic field have the same value as at a distance 0.5mm from the axis?
(a) 1.25mm (b) 1.5mm (c) 2mm (d) other
4. Find the magnetic energy stored in a toroid whose central line is 1m long, the cross sectional area is 10cm2 and the current is 2A. The toroid has 1000 turns.
(a) 0.46mJ (b) 0.91mJ (c) 2.52mJ (d) none
5. 10 turns of wire are tightly wound around a solenoid having a length of 12.56cm and a cross-sectional area of 5cm2. The number of turns of the solenoid is 200. Find the mutual inductance.
(a) 5H (b) 10H (c) 15H (d) none
6. Two slits at a distance of 0.4mm from each other are illuminated with blue light (=400nm). Find the distance between the interference fringes if the screen is 1 meter away from the slits.
(a) 1mm (b) 2mm (c) 10mm (d) none
7. Calculate the ratio between (1) the power incident on a 4mm2 surface at a distance 1 meter from a 25W light bulb, and (2) the power incident on the same surface if it is illuminated by a 1mW laser. The diameter of the laser beam is 1mm.
(a) 1/8 (b) 1/53 (c) 1/126 (d) none
8. An electron is confined to a 1D box in which its ground state energy is 2eV. How much energy is required to excite the electron into the next energy state?
(a) 2eV (b) 4eV (c) 6eV (d) none
9. Determine the number of electrons that can occupy the n=3 shell in an atom.
(a) 9 (b) 18 (c) 36 (d) none
10. Find the smallest possible value of the angle between the orbital angular momentum vector and an external magnetic field for an electron in a 3d state of hydrogen.
(a) 35 (b) 45 (c) 55 (d) none
II. True-false statements (1 point each):
1. According to Biot-Savart's law the magnetic field is inversely proportional to the cube of the distance from the current element.
F
2. The flux of for a closed surface is always zero.
T
3. The Hall-effect can be a useful tool for measuring the magnetic field.
T
4. If the net current across a surface bounded by a closed loop is zero, then the magnetic field is zero everywhere along the loop.
F
5. Paramagnetic materials cannot be gases or liquids.
F
6. The line integral of the magnetic field strength can be measured in W/V.
T
7. The mutual inductance depends on the applied current.
F
8. In Young's double slit experiment, when the illumination is white light, the zeroth-order fringe is in color.
F
9. When an incident light of any polarization comes at Brewster's angle, there is no reflection.
F
10. The resolution of an astronomical telescope is independent of the observed wavelength.
F
11. In blackbody radiation, the total emitted power is proportional to the fourth power of the temperature.
T
12. In blackbody radiation, the temperature multiplied by the maximal wavelength gives a universal constant.
F
13. Natural line broadening in a laser can be explained using Heisenberg's uncertainty principle.
T
14. Covalent bond is caused by the Coulomb attraction between two ions.
F
15. Knowing the rotational energy levels of a molecule gives us information about the bond strength.
F
III. Theory (3 points each):
1. What interpretational difficulties arise in relation with the magnetic permeability of ferromagnetic materials?
2. How can we produce linearly polarized light out of unpolarized light? (List at least 2 or 3 different methods.)
3. Why are at least 3 energy levels necessary in optical laser pumping?
4. What is Wien’s displacement law of blackbody radiation?
5. What is the physical meaning of the square of the absolute value of the wave function?
-
[math]q_e=1.6*10^{-19}C[/math]
[math]m_e=9.1*10^{-31}kg [/math]
[math] \mu_0=4\pi*10^{-7}\frac{Vs}{Am} [/math]
[math]E_0=8.85*10^{-12}\frac{As}{Vm} [/math]
[math]h=6.626*10^{-34}Js [/math]
