Question:
The maximum velocity to which a proton can be accelerated in a cyclotron of $ 10\, MHz $ frequency and radius $ 50\, cm $ is
The maximum velocity to which a proton can be accelerated in a cyclotron of $ 10\, MHz $ frequency and radius $ 50\, cm $ is
Updated On: Jun 14, 2022
- $ 6.28 \times 10^{8}\,m/s $
- $ 3.14 \times 10^{8}\,m/s $
- $ 6.28 \times 10^{7}\,m/s $
- $ 3.14 \times 10^{7}\,m/s $
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The Correct Option is D
Solution and Explanation
The motion of proton in magnetic field will be circular
$\therefore V=2\pi rf$
$=2\times3.14\times50\times10^{-2}\times10\times10^{6}$
$=3.14\times10^{7} m/s$
$\therefore V=2\pi rf$
$=2\times3.14\times50\times10^{-2}\times10\times10^{6}$
$=3.14\times10^{7} m/s$
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.