# Calculate Proton Energy in eV in Magnetic Field of 1.15T

• blue_soda025
In summary, to calculate the energy of a proton in a circular path perpendicular to a 1.15-T magnetic field with a radius of 8.40 mm, we first determine the velocity of the proton using the equation qvB = (mv^2)/r. Plugging in the values and solving for v, we get a velocity of 2.47 x 10^5 m/s. Then, using the equation E = qv, we can calculate the energy of the proton to be 3.95 x 10^-14 J. However, since we are looking for the energy in eV, we divide this value by the charge of an electron (1.60 x 10^-19). This gives
blue_soda025
A proton moves in a circular path perpendicular to a 1.15-T magnetic field. The radius of its path is 8.40 mm. Calculate the energy of the proton in eV.

So, I calculated the velocity with:
$$qvB = \frac{mv^2}{r}$$
$$(1.60 \times 10^-19)(1.15) = \frac{(6.27 \times 10^-27)v}{0.0084}$$
$$v = 2.47 \times 10^5 m/s$$
Then calculated the energy:
$$E = qv$$
$$E = (1.60 \times 10^-19)(2.47 \times 10^5)$$
$$E = 3.95 \times 10^-14 J$$
Then divided that by eV (1.60 x 10^-19) but I get something like 247000. The answer says 4.47 keV though. What am I doing wrong?

Mass of a proton is:$$1.67\times10^{-27}kg$$ not the number you used.

Also you have the wrong equation for energy. I think you took E=qV...where V is voltage not velocity... however that equation does not apply here.

The energy of the proton is kinetic energy... so use $$E=\frac{1}{2}mv^2$$

It seems like you may have made a mistake in your conversion from joules to electron volts. Remember, 1 eV is equal to 1.60 x 10^-19 joules. So, to convert from joules to eV, you need to divide by this conversion factor, not multiply. So, the correct calculation would be:

E = (3.95 x 10^-14 J) / (1.60 x 10^-19 J/eV) = 2.47 x 10^5 eV

This is the same value you got for the velocity, but you just need to divide by the conversion factor to get the correct answer in eV. So, the energy of the proton in this scenario would be 2.47 x 10^5 eV or 247 keV. This is very close to the given answer of 4.47 keV, so it seems like the discrepancy was just a conversion error.

## 1. What is the formula for calculating proton energy in eV in a magnetic field of 1.15T?

The formula for calculating proton energy in eV in a magnetic field of 1.15T is E = qBv, where E represents energy in electron volts, q is the charge of a proton (1.6 x 10^-19 C), B is the magnetic field strength in Tesla, and v is the velocity of the proton in meters per second.

## 2. Is it possible to convert the energy of a proton in eV to joules?

Yes, it is possible to convert the energy of a proton in eV to joules. The conversion factor is 1 eV = 1.6 x 10^-19 J.

## 3. How do I determine the velocity of a proton in a magnetic field of 1.15T?

The velocity of a proton in a magnetic field of 1.15T can be determined using the formula v = E/qB, where E is the energy in eV, q is the charge of a proton, and B is the magnetic field strength. Rearranging the formula, we get v = √(2E/m), where m is the mass of a proton (1.67 x 10^-27 kg).

## 4. Can the formula for calculating proton energy in eV be used for other charged particles?

Yes, the formula E = qBv can also be used to calculate the energy of other charged particles in a magnetic field of 1.15T. However, the charge and mass of the particle will be different.

## 5. How does the strength of the magnetic field affect the energy of a proton?

The strength of the magnetic field has a direct impact on the energy of a proton. As the magnetic field strength increases, the energy of the proton also increases. This is because the force on the proton increases, causing it to move with a greater velocity and therefore have more energy.

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