What speed would a proton need to orbit in an exact circle ?

AI Thread Summary
To determine the speed a proton needs to orbit Earth at a height of 476 km, the magnetic field intensity is given as 4.81 × 10−8 T, and the mass of the proton is 1.67262 × 10−27 kg. The formula used for calculating the velocity is v = (r*q*B)/m, where r is the radius of the orbit. A participant points out that the radius value used in the calculation is incorrect, emphasizing that it should represent the radius of the proton's path rather than the Earth's radius. Correcting this value is crucial for arriving at the accurate speed required for the proton's circular orbit.
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Homework Statement


Assume the Earth’s magnetic dipole moment
is aligned with the Earth’s rotational axis,
and the Earth’s magnetic field is cylindrically
symmetric (like an ideal bar magnetic).
What speed would a proton need to orbit in
an exact circle around the Earth at a height of
476 km, where the Earth’s magnetic field has
an intensity of 4.81 × 10−8 T? The mass of
a proton is 1.67262 × 10−27 kg and the radius
of Earth is 6.37 × 106 m.
Answer in units of m/s.


Homework Equations



r= m*v/(q*B)


The Attempt at a Solution



i solved for the velocity but it is wrong i think I'm missing a step =S
 
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From my perspective you're missing more than a step :wink: What did you get and how did you get it?
 
v= (r*q*B)/m
v=(6.3*10^6)(1.6*10^-19)(4.81*10^-8)/(1.67*10^-27)
 
mba444 said:
v= (r*q*B)/m
v=(6.3*10^6)(1.6*10^-19)(4.81*10^-8)/(1.67*10^-27)

I believe your value for r in this equation is incorrect. The value r is the radius of the particles path; do you see what it needs to be?
 
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