A cyclotron is used to accelerate protons. If the operating magnetic field is $1.0\,T$ and the radius of the cyclotron 'dees' is $60 cm$, the kinetic energy of the accelerated protons in $MeV$ will be.

[use $m _{p}=1.6 \times 10^{-27} kg , e =1.6 \times 10^{-19} C$ ]

JEE MAIN 2022, Medium
Download our app for free and get startedPlay store
Kinetic energy of electron in cyclotron

$=\left[\frac{ q ^{2} B ^{2} r _{0}^{2}}{2 m }\right]$

$=18\,MeV$

art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    The figure shows the cross section of a long cylindrical conductor through which an axial hole of radius $r$ is drilled with its centre at point $A$ . $O$ is the centre of the conductor. If an identical hole were to be drilled centred at point $B$ while maintaining the same current density the magnitude of magnetic field at $O$ 
    View Solution
  • 2
    A cyclotron is used to accelerate protons. If the operating magnetic field is $1.0\,T$ and the radius of the cyclotron 'dees' is $60 cm$, the kinetic energy of the accelerated protons in $MeV$ will be.

    [use $m _{p}=1.6 \times 10^{-27} kg , e =1.6 \times 10^{-19} C$ ]

    View Solution
  • 3
    A helium nucleus makes a full rotation in a circle of radius $0.8$ metre in two seconds. The value of the magnetic field $B$ at the centre of the circle will be
    View Solution
  • 4
    A wire carrying $I$ is shaped as shown. Section $AB$ is a quarter circle of radius $r.$ The magnetic field at $C$ is directed
    View Solution
  • 5
    The current sensitivity of moving coil galvanometer is increased by $25 \%$. This increase is achieved only by changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be $...........\%$
    View Solution
  • 6
    Given below are two statements$:$

    Statement $I:$ Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (IdI) of a current carrying conductor only.

    Statement $II :$ Biot-Savart's law is analogous to Coulomb's inverse square law of charge $q$, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, $q$. In light of above statements choose the most appropriate answer from the options given below:

    View Solution
  • 7
    Two long parallel wires are at a distance $R$ apart. They carry steady equal currents in the same directions as shown in the figure. The ratio of magnetic fields at $A, B$ and $C$ respectively, is
    View Solution
  • 8
    Two infinitely long parallel wires carry currents of magnitude $I_1$ and $I_2$ are at a distance $4 cm$ apart. The magnitude of the net magnetic field is found to reach a non-zero minimum value between the two wires and $1 \,cm$ away from the first wire. The ratio of the two currents and their mutual direction is
    View Solution
  • 9
    A winding wire which is used to frame a solenoid can bear a maximum $10\, A$ current. If length of solenoid is $80\,cm$ and it's cross sectional radius is $3\, cm$ then required length of winding wire is $(B = 0.2\,T)$
    View Solution
  • 10
    A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\overrightarrow E $ and $\overrightarrow B $ represent the electric and magnetic fields respectively, then this region of space may have
    View Solution