Up to what values of kinetic energy does the period of revolution of an electron and a proton in a uniform magnetic field exceed that at non-relativistic velocities by $$\eta = 1.0\%$$?
$$T = \dfrac {2\pi \epsilon}{c^{2}eB} (relativistic), T_{0} = \dfrac {2\pi \ m_{0}c^{2}}{c^{2}eB} (nonrelativistic)$$,
Here, $$m_{0}c^{2} / \sqrt {1 - v^{2}/c^{2}} = E$$
Thus, $$\delta T = \dfrac {2\pi T}{c^{2}eB}, (T = K.E.)$$
Now, $$\dfrac {\delta T}{T_{0}} = \eta = \dfrac {T}{m_{0}c^{2}}$$, so, $$T = \eta m_{0}c^{2}$$.
A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of 100 V/m makes it move in a straight path, then the mass of the particle is ___? (Given charge of electron = $$1.6 \times 10^{-19} C$$)
An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $$r_e, r_p, r_{\alpha}$$ respectively in a uniform magnetic field B. The relation between $$r_e, r_p, r_{\alpha}$$ is?
When a charged particle is acted on only by a magnetic force, its:
A proton carrying $$1MeV$$ kinetic energy is moving in a circular path of radius $$R$$ in uniform magnetic field. What should be the energy of an $$\alpha$$-particle to describe a circle of same radius in the same field?
A proton and alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be:
If an electron describes half a revolution in a circle of radius $$r$$ in a magnetic field $$B$$, the energy acquire by it is :
An electron starts moving in a uniform electric field of strength $$E = 10\ kV/cm$$. How soon after the start will the kinetic energy of the electron become equal to its rest energy?
Protons are accelerated in a cyclotron so that the maximum curvature radius of their trajectory is equal to $$r = 50\ cm$$. Find : (a) the kinetic energy of the protons when the acceleration is completed if the magnetic induction in the cyclotron is $$B = 1.0\ T$$; (b) the minimum frequency of the cyclotron's oscillator at which the kinetic energy of the protons amounts to $$T = 20\ MeV$$ by the end of acceleration.
In a betatron the magnetic induction on an equilibrium orbit with radius $$r = 20\ cm$$ varies during a time interval $$\triangle t = 1.0\ ms$$ at parctically constant rate from zero to $$B = 0.40\ T$$. Find the energy acquired by the electron per revolution.
The magnetic induction in a betatron on an equilibrium orbit of radius $$r$$ varies during the acceleration time at practically constant rate from zero to $$B$$. Assuming the initial velocity of the electron to be equal to zero, find: (a) the energy acquired by the electron during the acceleration time; (b) the corresponding distance covered by the electron if the acceleration time is equal to $$\triangle t$$.