A Tevatron can accelerate particles to energies in the TeV range (1.00 tera −eV = 1.00×10^12 eV ). Its circumference is 6.40 km, and in a certain medical experiment protons will be accelerated to energies of 1.25 MeV and aimed at a tumor to destroy its cells.
1) How fast are these protons moving when they hit the tumor?
v = 1.55×107 m/s (correct answer)
2) How strong must the magnetic field be to bend the protons in the circle indicated?
So I know that F = qv x B and that
B = mu*I / 2pi*r
The answer needs to be B equals some amount in T, but I don't have the charge (I). What should I do?
google these ... mass of proton, charge of proton, Joules to MeV
current*, not charge
I'm not sure I can concert the voltages into amps without knowing power
one MeV is 1.60E-13 Joules
proton mass is 1.67E-27 kg
1/2 m v^2 = 1.25 * 1.60E-13 J = 2.00E-13
v^2 = 2 * 2.00E-13 / 1.67E-27
v = 1.55E7 m/s
proton charge is 1.60E-19 C
... same as electron, opposite polarity
current is charge per unit time past a given point ... C / s
the circumference of the ring is
... 6.40E3 m
the current from a proton is
... (1.60E-19) / (6.40E3 / 1.55E7)
To determine the strength of the magnetic field required to bend the protons in the circle, you need to use the relationship between the magnetic field, charged particle's velocity, charge, and radius of curvature.
The equation you mentioned, F = qv x B, is used to calculate the magnetic force exerted on a charged particle moving through a magnetic field. In this case, the force required to bend the protons in a circular path is provided by the equation:
F = mv^2 / r
Where:
F is the centripetal force,
m is the mass of the proton,
v is the velocity of the proton, and
r is the radius of the circular path.
Since you're given the energy of the protons (1.25 MeV), you can use the relationship E = mv^2 / 2 to find the velocity of the protons:
v = √(2E / m)
Now, you mentioned that the Tevatron has a circumference of 6.40 km. The radius of the circular path can be calculated using the formula:
r = circumference / (2π)
So, once you have the value of r and the velocity of the protons, you can now calculate the strength of the magnetic field, B:
B = F / (qv)
However, you correctly pointed out that you don't have the charge of the protons (q). In this case, you can use the charge-to-mass ratio (q/m) of the protons, which is a known constant. The charge-to-mass ratio for protons is approximately 1.602 × 10^-19 C/kg.
Therefore, you can now calculate the magnetic field required using the equation:
B = (mv) / (q/2πr)
Substituting the values you have:
B = (m√(2E/m)) / (q/2πr)
Simplifying further:
B = (2πr√(2E/m)) / q
Now, plug in the known values:
- Mass of proton (m) is approximately 1.673 × 10^-27 kg
- Energy of protons (E) is 1.25 MeV, which can be converted to joules by multiplying by 1.602 × 10^-13 (since 1.00 MeV = 1.602 × 10^-13 J)
- Charge-to-mass ratio (q/m) is 1.602 × 10^-19 C/kg
- Radius (r) is 6.40 km, which can be converted to meters by multiplying by 1000
After substituting these values into the equation, you can calculate the strength of the magnetic field (B) in Tesla (T).