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

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Homework Help Overview

The problem involves calculating the speed required for a proton to orbit the Earth in a circular path at a specific height, considering the Earth's magnetic field and the properties of the proton. The context includes elements of electromagnetism and circular motion.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formula for velocity in the context of magnetic fields and circular motion. There is an attempt to solve for velocity, but questions arise regarding the correctness of the radius used in the calculations.

Discussion Status

The discussion is ongoing, with participants providing feedback on the attempts made. There is an indication that some values may need reconsideration, particularly regarding the radius in the equation.

Contextual Notes

Participants are working under the assumption that the magnetic field is cylindrically symmetric and that the height of the orbit is fixed. There may be confusion regarding the appropriate radius to use in the calculations.

mba444
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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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