Question:
The cyclotron frequency of an electron grating in a magnetic field of $1 \,T$ is approximately
The cyclotron frequency of an electron grating in a magnetic field of $1 \,T$ is approximately
Updated On: Jun 18, 2022
- 28 MHZ
- 280 MHZ
- 2.8 GHZ
- 28 GHZ
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The Correct Option is D
Solution and Explanation
For a cyclotron, frequency is given by,
$v=\frac{ Be }{2 \pi m _{ e }}=\frac{1 \times 1.6 \times 10^{-19}}{2 \pi \times 9.1 \times 10^{-31}}$
$=28 \times 10^{9} \,Hz =28\, GHz$
$v=\frac{ Be }{2 \pi m _{ e }}=\frac{1 \times 1.6 \times 10^{-19}}{2 \pi \times 9.1 \times 10^{-31}}$
$=28 \times 10^{9} \,Hz =28\, GHz$
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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.