Advertisements
Advertisements
Question
Which of the following particles will describe the smallest circle when projected with the same velocity perpendicular to a magnetic field?
Options
Electron
Proton
He+
Li+
Solution
Electron
When a particle moves in a magnetic field, the necessary centripetal force, for the particle to move in a circle, is provided by the magnetic force acting on the particle.
So, equating the Lorentz force with the cetripetal force for a charged particle of charge q describing a circle of radius r, we get:
`qvB = (mv^2)/r`
`⇒ r = "(mv)"/"qB"`
Here, m is the mass of the particle and v is its velocity.
The amount of charge of all the given particles is same; hence, for a given charge, r ∝ m . And since the electron is the lightest of all the particles, it describes the smallest circle when projected with the same velocity perpendicular to the magnetic field.
APPEARS IN
RELATED QUESTIONS
Draw a neat labelled diagram for the construction of 'cyclotron'
State the principle of a cyclotron.
Show that the time period of revolution of particles in a cyclotron is independent of their speeds. Why is this property necessary for the operation of a cyclotron?
Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.
If a watch-glass containing a small quantity of water is placed on two dissimilar magnetic poles, then water ______.
Obtain the expression for the cyclotron frequency.
Figure shows a rod PQ of length 20.0 cm and mass 200 g suspended through a fixed point O by two threads of lengths 20.0 cm each. A magnetic field of strength 0.500 T exists in the vicinity of the wire PQ, as shown in the figure. The wires connecting PQ with the battery are loose and exert no force on PQ. (a) Find the tension in the threads when the switch S is open. (b) A current of 2.0 A is established when the switch S is closed. Find the tension in the threads now.
\[\ce{Fe+}\] ions are accelerated through a potential difference of 500 V and are injected normally into a homogeneous magnetic field B of strength 20.0 mT. Find the radius of the circular paths followed by the isotopes with mass numbers 57 and 58. Take the mass of an ion = A (1.6 × 10−27) kg, where A is the mass number.
A cyclotron's oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its 'dees' is 60 cm, calculate the kinetic energy (in MeV) of the proton beam produced by the accelerator.
Cyclotron frequency of a charged particle having charge q and mass m in a cyclotron producing magnetic field B is ______.
Assertion: The frequency of circular motion of a charged particle in cyclotron is independent of the mass of the particle.
Reason: Greater the mass of the particle less will be the frequency of the particle.
A charged particle is moving in a cyclotron, what effect on the radius of path of this charged particle will occur when the frequency of the ratio frequency field is doubled?
A particle of mass m is moving in a circular path of constant radius r such that, its centripetal acceleration ac is varying with time t as ac = k2rt2, where k is a constant. The power delivered to the particle by the forces acting on it is ______.
The life time of muon in the rest frame is 2 × 10-6 sec. A beam of muons emerges from a cyclotron with velocity where c is the velocity of light The mean life of muons observed in the laboratory frame will be ______.
The cyclotron was designed by ______
Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.
