Physics problem - 3154
2017-04-30
A particle with mass $m = 6.65 \cdot 10^(-27) kg$ and charge $q = 3.2 \cdot 10^(-19) C$ is first accelerated in an electrostatic field, passing through an accelerating potential difference $u = 2500 In $. starting speed particles is zero. Then the particle flies into a uniform magnetic field with induction $B = 210 T$, perpendicular to the velocity vector. Find the change in momentum of the particle over time $t = \frac( \pi)(2) \cdot 1.039 \cdot 10^(-3) s$ after entering the magnetic field. Determine the magnitude of the centripetal and tangential acceleration of the particle at this and subsequent times.
X-ray small-scale scattering. This is a diffraction technique widely used to study the superatomic structure of substances. It is used in condensed matter physics, analysis of dispersion systems, molecular biology, biophysics, polymer research, metallurgy and other fields of science and technology.
The use of X-rays in forensics, archaeology, customs control. Studies of the structure of crystalline, non-crystalline, liquid substances, polymers. Diffraction of characteristic X-ray radiation allows one to fully study the crystal structure of a substance.
Solution:
Let at the initial moment of time the charged particle be at point A electrostatic field, whose potential is equal to $\phi_(A)$. Then the particle energy is the potential energy in the electrostatic field $W_(A) = W_(pA) = q \phi_(A)$. At point B, the particle energy consists of potential $W_(pB) = q \phi_(B)$ and kinetic $W_(kB) = \frac(mv^(2))(2)$, i.e. $W_(B) = q \phi_(B) + \frac(mv^(2))(2)$. According to the law of conservation of energy $W_(A) = W_(B) \Rightarrow q \phi_(A) = q \phi_(B) + \frac(mv^(2))(2) \Rightarrow q(\phi_(A ) - \phi_(B)) = \frac(mv^(2))(2)$.
X-ray radiation in physics and plasma technology. Plasma is a source of optical and x-ray radiation. X-ray studies consist of measuring changes over time in radiation efficiency and its spectral distribution. The intensity of bremsstrahlung generated by electrons with a Maxwellian distribution is equal.
And thus, determining the slope of this line as a function of photon energy gives the electron temperature T, and the intensity gives information about the density of electrons and ions. Use of synchrotron radiation. Synchrotron radiation was originally produced in synchrotrons, and now so-called storage rings. He has a lot important functions.
But $\phi_(A) - \phi_(B) = u \Rightarrow qu = \frac(mv^(2))(2)$, and the speed of a particle when it enters a magnetic field $v = \sqrt( \frac (2qu)(m)) = 4.9 \cdot 10^(5) m/s$. In a magnetic field, a particle under the influence of the Lorentz force moves in a circle with a constant velocity $v$ (Fig.). According to Newton's second law, $F_(l) = m \cdot a_(n)$, where the Lorentz force $F_(l)= qvB$, and the centripetal acceleration of the particle $a_(n) = \frac(v^(2)) (R)$. After substitution we obtain $qvB = m \frac(v^(2))(R)$, from which the radius of the circle $R = \frac(mv)(qB) = 510 m$. The period of revolution of a particle along a circle $T = \frac(2 \pi R)(v) = \frac(2 \pi m)(qB) = 2 \pi \cdot 1.039 \cdot 10^(-3) s$.
The continuous spectrum ranges from infrared to hard x-rays. This radiation is very highly collimated and polarized. The emission time of this radiation is 0.1 ns with a repeatability of 1 ns to 1 ms, which is important for studying dynamics.
Measurement of some physical constants. Measuring the Planck Constant To measure the Planck constant, you can use a wavelength corresponding to the short-term limit of the bremsstrahlung spectrum. This boundary is related to the energy of the electrons inducing this radiation with a dependence.
Ratio of movement time $t$ to period
$\frac(t)(T) = \frac( \left (\frac( \pi)(2) \cdot 1.039 \cdot 10^(-3) \right) )( 2 \pi \cdot 1.039 \cdot 10 ^(-3)) = \frac(1)(4) \Rightarrow t = \frac(1)(4) T$, i.e. behind specified time the particle passes 1/4 of the circle, and its velocity vector rotates by $90^( \circ)$ (Fig.). 
Momentum change $\Delta \vec(p) = \vec(p)_(2) - \vec(p)_(1) = \vec(p)_(2) + (- \vec(p)_( 1))$, where $p_(1) = p_(2) = mv$.
Avogadro's measurement Avogadro can be used to diffraction characteristic X-rays from a crystal of known structure. Avogadro's number refers to the number of atoms contained in one mole of a substance. X-ray spectroscopy is a branch of physics that involves the study of the structure and properties of molecules, atoms and atomic nuclei and interactions of atoms and molecules based on the electromagnetic radiation they emit.
X-ray emission spectroscopy. X-ray absorption spectroscopy. This allows one to study the local structure of the atom of this type in a material based on fluctuations in the absorption coefficient up to 50 eV of energy above the absorption edge and above 50 eV. However, they require high radiation intensity and therefore synchrotron radiation is mainly used. X-ray photoelectron spectroscopy. Its principle is based on the study of the properties of photoelectrons emitted by the test sample under the influence of monoenergetic photons.
Vector modulus $\Delta p = \sqrt(2) p_(1) = \sqrt(2) p_(2) = 4.6 \cdot 10^(21) kgm/s$. Modulus of centripetal acceleration at any point on the circle
$a_(n) = \frac(v^(2))(R) = 4.7 \cdot 10^(8) m/s^(2)$.
Since the Lorentz force acting on the particle is directed along the radius of the circle towards the center, the tangential acceleration at any point $a_( \tau) = 0$.
Test on the topic:
This makes it possible to study the states of valence electrons and atomic nuclei of the nucleus. In this method, a beam of X-rays of known energy is incident on a sample, which knocks out electrons through the photoelectric effect. This method involves testing thin layers of a sample: the thickness of the analyzed metal layer is 0.5-2 nm, inorganic substances 1-3 nm and organic 3-10 nm. Synchrotron spectroscopy A synchrotron radiation source is a synchrotron or cyclic accelerator in which particles move in an increasing magnetic field, accelerated by an alternating electric field synchronized with their movement along a circular path.
Grade 11
Option 1
A1. What explains the interaction of two parallel conductors with direct current?
interaction of electric charges;
the effect of the electric field of one conductor with current on the current in another conductor;
action magnetic field one conductor to the current in another conductor.
on a moving charged one;
on a moving uncharged one;
to a stationary charged one;
to an uncharged one at rest.
A4. A straight conductor 10 cm long is in a uniform magnetic field with an induction of 4 T and is located at an angle of 30 0 to the magnetic induction vector. What is the force acting on the conductor from the magnetic field if the current in the conductor is 3 A?
This technique is used to study the electronic structure of atoms, molecules and solids and radiometry to calibrate radiation sources and detectors. Debye temperature measurement and atomic displacement in solids. Research on the distribution of electron density and electron momentum density. The electron density distribution is obtained using diffraction patterns of characteristic X-ray radiation. This is important not only for determining the structure of a substance, but also for checking interatomic bonds.
The electron momentum density is determined by Compton scattering of photons or electrons. Launching sounding rockets over earth's atmosphere, which absorbs radially X-rays, led to the discovery large quantity sources of this radiation. Most of them are associated with our galaxy, but a number, including the most powerful, are located outside of it. The strong source in the Crab Nebula and the Cas A source have the same brightness. It appears that the X-rays emitted by these sources are primarily responsible for two mechanisms: radiation inhibition and synchrotron formation.
1.2 N; 2) 0.6 N; 3) 2.4 N.
| A5. |  |
a phenomenon characterizing the effect of a magnetic field on a moving charge;
phenomenon of occurrence in closed loop electric current when the magnetic flux changes;
a phenomenon characterizing the effect of a magnetic field on a current-carrying conductor.
1.2 A; 2) 0.6 A; 3) 2A.
IN 1.
| VALUES | UNITS |
||
| A) | inductance | 1) | tesla (T) |
| B) | magnetic flux | 2) | henry (Gn) |
| IN) | magnetic field induction | 3) | weber (Wb) |
| 4) | volt (V) |
||
AT 2. Particle with mass m, carrying charge q B circumferential radius R with speed v. What happens to the orbital radius, orbital period, and kinetic energy of the particle as its speed increases?
| PHYSICAL QUANTITIES | THEIR CHANGES |
||
| A) | orbital radius | 1) | will increase |
| B) | circulation period | 2) | will decrease |
| IN) | kinetic energy | 3) | Will not change |
C1. In a coil whose inductance is 0.4 H, a self-inductive emf of 20 V has arisen. Calculate the change in current strength and energy of the magnetic field of the coil if this happened in 0.2 s.
Test on the topic:
"A magnetic field. Electromagnetic induction"
Grade 11
Option 2
A1. The rotation of a magnetic needle near a current-carrying conductor is explained by the fact that it is affected by:
magnetic field created by charges moving in a conductor;
electric field created by charges on a conductor;
electric field created by moving charges of a conductor.
only electric field;
both electric field and magnetic field;
only magnetic field.
|
A3. Which of the figures correctly shows the direction of induction of the magnetic field created by a straight conductor carrying current?
|  |
A4. A straight conductor 5 cm long is in a uniform magnetic field with an induction of 5 T and is located at an angle of 30 0 to the magnetic induction vector. What is the force acting on the conductor from the magnetic field if the current in the conductor is 2 A?
0.25 N; 2) 0.5 N; 3) 1.5 N.
| A5. There is a current-carrying conductor in a magnetic field. What is the direction of the Ampere force acting on the conductor?
|  |
A6. The Lorentz force acts
on an uncharged particle in a magnetic field;
to a charged particle at rest in a magnetic field;
on a charged particle moving along the lines of magnetic induction field.
1)1 T; 2) 2 T; 3) 3T.
IN 1. Establish a correspondence between physical quantities and the formulas by which these quantities are determined
|
VALUES | UNITS |
||
| A) | Force acting on a current-carrying conductor from a magnetic field | 1) | |
| B) | Magnetic field energy | 2) | |
| IN) | The force acting on an electric charge moving in a magnetic field. | 3) | |
| 4) | |
||
AT 2. Particle with mass m, carrying charge q, moves in a uniform magnetic field with induction B circumferential radius R with speed v. What happens to the orbital radius, orbital period, and kinetic energy of the particle as the particle's charge increases?
For each position in the first column, select the corresponding position in the second and write down the selected numbers in the table under the corresponding letters
| PHYSICAL QUANTITIES | THEIR CHANGES |
||
| A) | orbital radius | 1) | will increase |
| B) | circulation period | 2) | will decrease |
| IN) | kinetic energy | 3) | Will not change |
C1. At what angle to power lines magnetic field with an induction of 0.5 T, a copper conductor with a cross section of 0.85 mm 2 and a resistance of 0.04 Ohm must move so that at a speed of 0.5 m/s an induced emf equal to 0.35 V is excited at its ends? ( resistivity copper ρ= 0.017 Ohm∙mm 2 /m)
Test on the topic:
"A magnetic field. Electromagnetic induction"
Grade 11
Option 3
A1. Magnetic fields are created:
both stationary and moving electric charges;
stationary electric charges;
moving electric charges.
A2. The magnetic field affects:
only on stationary electric charges;
only on moving electric charges;
both moving and stationary electric charges.
A4. What force acts from a uniform magnetic field with an induction of 30 mT on a straight conductor 50 cm long located in the field, carrying a current of 12 A? The wire forms a right angle with the direction of the magnetic field induction vector.
18 N; 2) 1.8 N; 3) 0.18 N; 4) 0.018 N.
| A5. There is a current-carrying conductor in a magnetic field. What is the direction of the Ampere force acting on the conductor? 1)up; 2) down; 3) left; 4) to the right. |  |
A6. What do the four outstretched fingers of the left hand show when determining
Ampere forces
direction of field induction force;
direction of current;
direction of the Ampere force.
1m; 2) 0.1 m; 3) 0.01 m; 4) 0.001 m.
| VALUES | UNITS |
||
| A) | current strength | 1) | weber (Wb) |
| B) | magnetic flux | 2) | ampere (A) |
| IN) | induced emf | 3) | tesla (T) |
| 4) | volt (V) |
||
AT 2. Particle with mass m, carrying charge q, moves in a uniform magnetic field with induction B circumferential radius R with speed v. What happens to the orbital radius, orbital period, and kinetic energy of the particle as the magnetic field induction increases?
For each position in the first column, select the corresponding position in the second and write down the selected numbers in the table under the corresponding letters
| PHYSICAL QUANTITIES | THEIR CHANGES |
||
| A) | orbital radius | 1) | will increase |
| B) | circulation period | 2) | will decrease |
| IN) | kinetic energy | 3) | Will not change |
C1. In a coil consisting of 75 turns, the magnetic flux is 4.8∙10 -3 Wb. How long does it take for this flux to disappear for an average induced emf of 0.74 V to arise in the coil?
Test