Question
Explain cyclotron motion and cyclotron formula.
✓
Answer
Suppose a particle of mass $m$ and charge $q$ enters a region of uniform magnetic field of induction $\vec{B}$. In below figure, $\vec{B}$ points into the page. The magnetic force $\vec{F}_{ m }$ on the particle is always perpendicular to the velocity of the particle, $\vec{v}$. Assuming the charged particle started moving in a plane perpendicular to $\vec{B}_r$ its motion in the magnetic field is a uniform circular motion, with the magnetic force providing the centripetal acceleration.
where $p=m v$ is the linear momentum of the particle. Equation (1) is known as the cyclotron formula because it describes the motion of a particle in a cyclotron-the first of the modern particle accelerators.
where $p=m v$ is the linear momentum of the particle. Equation (1) is known as the cyclotron formula because it describes the motion of a particle in a cyclotron-the first of the modern particle accelerators.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Calculate the binding energy of an alpha particle given its mass to be $4.00151\ u.$
→Derive an expression for energy stored in a charged capacitor.
A spherical metal ball of radius $15 \ cm$ carries a charge of $2 \mu C$. Calculate the electric field at a distance of $20 \ cm$ from the center of the sphere.
→A spherical metal ball of radius $15 \ cm$ carries a charge of $2 \mu C$. Calculate the electric field at a distance of $20 \ cm$ from the center of the sphere.
Derive the fiornsila for Aruwster's afyle.
Green light of wuelengths $100 A$ from a narrow sht is incident on a doubile dit. If the overall separation of $10$ fringes on a screen $2$ waway is $2 \ cm$ Find the slit separation.
→Green light of wuelengths $100 A$ from a narrow sht is incident on a doubile dit. If the overall separation of $10$ fringes on a screen $2$ waway is $2 \ cm$ Find the slit separation.
Derive an expression for the impedance of an $LCR$ circuit connected to an $AC$ power supply.
→Derive the expression for the average pressure of an ideal gas.
Resistances $P=10 \Omega, Q=15 \Omega, S=50 \Omega$ and $R=25 \Omega$ are connected in order in the arms
$\text{AB, BC, CD}$ and $\text{DA}$ respectively of a Wheatstone network $\text{ABCD}$. A cell is connected between $A$ and $C$. What resistance has to be connected in parallel to $S$ to balance the network?
→$\text{AB, BC, CD}$ and $\text{DA}$ respectively of a Wheatstone network $\text{ABCD}$. A cell is connected between $A$ and $C$. What resistance has to be connected in parallel to $S$ to balance the network?
White Light LEDs or White LED Lamps:
Shuji Nakamura, a Japanese – born American electronic engineer invented the blue LED. He was awarded the Nobel prize for physics for 2014. He was also awarded the global energy prize in the year 2015. His invention of blue LED made the fabrication of white LED possible.
LED lamps, bulbs, street lighting are becoming very popular these days because of the very high efficiency of LEDs in terms of light output per unit input power(in milliWatts), as compared to the incandescent bulbs. So for general purpose lightings, white light is preferred.
Commercially available white LEDs are normally manufactured by using the technique of wavelength conversion. It is a process which partly or completely converts the radiation of a LED into white light. There are many ways of wavelength conversion. One of these methods uses blue LED and yellow phosphor. In this method of wavelength conversion, a LED which emits blue colour is used to excite a yellow colour phosphor. This results in the emission of yellow and blue light and this mixture of blue and yellow light gives the appearance of white light. This method is the least expensive method for producing white light.
Shuji Nakamura, a Japanese – born American electronic engineer invented the blue LED. He was awarded the Nobel prize for physics for 2014. He was also awarded the global energy prize in the year 2015. His invention of blue LED made the fabrication of white LED possible.
LED lamps, bulbs, street lighting are becoming very popular these days because of the very high efficiency of LEDs in terms of light output per unit input power(in milliWatts), as compared to the incandescent bulbs. So for general purpose lightings, white light is preferred.
Commercially available white LEDs are normally manufactured by using the technique of wavelength conversion. It is a process which partly or completely converts the radiation of a LED into white light. There are many ways of wavelength conversion. One of these methods uses blue LED and yellow phosphor. In this method of wavelength conversion, a LED which emits blue colour is used to excite a yellow colour phosphor. This results in the emission of yellow and blue light and this mixture of blue and yellow light gives the appearance of white light. This method is the least expensive method for producing white light.
An ion of mass re and charge $q$ is accelerated from rest through a potential difference $V$ and enters a region of uniform magnetic field of induction $B.$ Within the region, the ion moves in a semidrcle and strikes a photographic plate which lies along the diameter of the semicircle at a distance $D$ from the point of entry. Show that the mass of the ion is given by $m=k \frac{q D^2 B^2}{V}$
→Due to a single charge at a distance r, Force $(F ) α 1/r^2$, Electric field $(E ) \alpha 1/r^2$ but Potential $(V) α 1/ r$.
→Assuming the Stefan-Boltzmann law, compare the rate of radiation from a metal ball at 727 ${ }^{\circ} \mathrm{C}$ with its rate of radiation at $527^{\circ} \mathrm{C}$. Also compare its rate of loss of heat at the two temperatures, if the temperature of the surroundings is $27^{\circ} \mathrm{C}$.
→