Synch/Cyclotron equations help

• ScotchDave
In summary, the formula for cyclotronic motion in SI units is p=qeBR, and in units in which R is in meters and p is in GeV/c, it is p=0.3qBR.
ScotchDave

Homework Statement

The formula for cyclotronic motion in SI units was shown to be p=qeBR. Show that in units in which R is in metres but p is in GeV/c p=0.3qBR

Homework Equations

$$qe^{-}=1.6 \times 10^{-19} C$$ I think!

$$L=\frac{\hbar \times c}{eV}= 1.9732705 \times 10^{-7} m$$ I think!

$$B = 1 eV^{2} = 1.44 \times 10^{-3} Teslas$$ I think!

The Attempt at a Solution

So, now I get even MORE confused and try substituting stuff in, but don't get anywhere!

$$p = \frac{10^{9}}{1.6 \times 10^{-19} \times 1.97x10^{-7} \times 1.44\times10^{-3}}} = 2.2 \times 10^{37}$$

or
$$p = \frac{10^{9} \times1.6 \times 10^{-19}}{ 1.97x10^{-7} \times 1.44\times10^{-3}}} = 0.56$$
This is clearly wrong, but I'm just getting COMPLETELY confused by all of this. Can anyone help me please?

Last edited:

First, let's clarify the units for the given quantities:
- p is the momentum, which is typically measured in units of kg*m/s. However, in this problem, we are using p in units of GeV/c, which is a unit of momentum commonly used in particle physics. 1 GeV/c is equal to 1.6 x 10^-10 kg*m/s.
- q is the charge of the particle, which is measured in units of Coulombs (C).
- e is the elementary charge, which is equal to 1.6 x 10^-19 C.
- B is the magnetic field, which is measured in units of Teslas (T).
- R is the radius of the circular path, which is measured in units of meters (m).

Now, let's substitute these units into the given formula:
p = qeBR
p = (1.6 x 10^-10 kg*m/s)(C)(T)(m)
p = (1.6 x 10^-10 kg*m/s)(1.6 x 10^-19 C)(1 T)(m)
p = (1.6 x 10^-29 kg*m^2/s^2)(m)
p = 1.6 x 10^-29 kg*m^3/s^2
p = 1.6 x 10^-29 GeV/c

This is not quite the desired form of p=0.3qBR, but we can convert this to the desired units of GeV/c by dividing by the conversion factor of 1.6 x 10^-10 kg*m/s:
p = (1.6 x 10^-29 GeV/c)(1/1.6 x 10^-10 kg*m/s)
p = 0.3 GeV/c

Therefore, in units in which R is in meters and p is in GeV/c, the formula for cyclotronic motion can be written as p=0.3qBR.

1. What are the Synch/Cyclotron equations?

The Synch/Cyclotron equations are mathematical formulas used to describe the motion of charged particles in a magnetic field. They are used in particle accelerators and other high-energy physics applications.

2. Why are the Synch/Cyclotron equations important?

The Synch/Cyclotron equations are important because they allow scientists to accurately predict the trajectory and energy of charged particles in a magnetic field. This is crucial for designing and operating particle accelerators and studying the behavior of particles in high-energy physics experiments.

3. How do the Synch/Cyclotron equations work?

The Synch/Cyclotron equations take into account the Lorentz force, which describes the interaction between a charged particle and a magnetic field. By solving these equations, scientists can determine the radius, frequency, and energy of a particle's circular motion in a magnetic field.

4. What are some applications of the Synch/Cyclotron equations?

The Synch/Cyclotron equations have a wide range of applications in physics, including particle accelerators, particle beam therapy, and magnetic resonance imaging (MRI). They are also used in space science to study the behavior of charged particles in Earth's magnetic field and the magnetic fields of other planets.

5. Are the Synch/Cyclotron equations difficult to understand?

The Synch/Cyclotron equations can be complex and require a strong understanding of mathematics and physics to fully comprehend. However, with proper training and practice, they can be understood and applied by scientists and engineers in various fields.

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