Calculate Proton Speed for Earth Magnetic Equator - Magnetism Question 2

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In summary, to circle Earth 1670 km above the magnetic equator with an intensity of 4.1 × 10−8 T, a proton would need a speed of 2.1 x 10^6 m/s. This can be solved by equating the centripetal force (f2) to the gravitational force (f3) and solving for velocity. The mass of a proton is 1.673 × 10−27 kg and the distance (d) is 1670 km, with R being the Earth's distance.
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tayi
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Homework Statement



What speed would a proton need to achieve
in order to circle Earth 1670 km above the
magnetic equator, where the Earth’s mag-
netic field is directed on a line between mag-
netic north and south and has an intensity of
4.1 × 10−8 T?
The mass of a proton is 1.673 × 10−27 kg.
Answer in units of m/s.

Homework Equations



f1=qvbsin(theta)
f2=mv^2/(d+R)
f3=Gm(proton)m(earth)/(d+R)^2 where d is 1670 km, and R is Earth distance


The Attempt at a Solution



I tried doing f1+f2=f3, b ut I am not sure if this is right and i don't know how to solve for v
 
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  • #2
I think you'd want to equate f2 to f3 as the gravitational force of attraction will provide the centripetal force.
 

1. What is the formula for calculating proton speed at Earth's magnetic equator?

The formula for calculating proton speed at Earth's magnetic equator is v = Bq/m, where v is the speed in meters per second, B is the magnetic field strength in Tesla, q is the charge of the proton in Coulombs, and m is the mass of the proton in kilograms.

2. How do you determine the magnetic field strength at Earth's magnetic equator?

The magnetic field strength at Earth's magnetic equator can be determined using a magnetometer, which measures the Earth's magnetic field. The data collected can then be used to calculate the strength of the magnetic field at that location.

3. What is the charge and mass of a proton?

The charge of a proton is +1.602 x 10^-19 Coulombs, and the mass is 1.6726 x 10^-27 kilograms.

4. Why is it important to calculate proton speed at Earth's magnetic equator?

Calculating proton speed at Earth's magnetic equator is important because it helps us understand the behavior of charged particles in Earth's magnetic field. This information is crucial for many scientific fields, such as space weather forecasting and understanding the effects of solar storms on Earth's atmosphere.

5. Are there any other factors that may affect the speed of protons at Earth's magnetic equator?

Yes, there are other factors that may affect the speed of protons at Earth's magnetic equator, such as the strength and direction of the magnetic field, the presence of other charged particles, and the energy of the protons themselves. These factors can all impact the overall behavior of protons in Earth's magnetic field.

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