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

In summary, the question asks for the speed a proton would need to orbit in an exact circle around the Earth at a height of 476 km, given that the Earth's magnetic field has an intensity of 4.81 × 10−8 T. The equation r= m*v/(q*B) is used to solve for the velocity, where r is the radius, m is the mass of the proton, q is the charge of the proton, and B is the magnetic field. The incorrect attempt at a solution used a value of 6.3 * 10^6 for r, but the correct value should be 6.37 * 10^6.
  • #1
mba444
54
0

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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  • #2
From my perspective you're missing more than a step :wink: What did you get and how did you get it?
 
  • #3
v= (r*q*B)/m
v=(6.3*10^6)(1.6*10^-19)(4.81*10^-8)/(1.67*10^-27)
 
  • #4
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?
 

1. What is a proton?

A proton is a subatomic particle with a positive charge and a mass approximately 1836 times greater than that of an electron. It is one of the fundamental particles that make up the atom.

2. What is meant by orbiting in an exact circle?

Orbiting in an exact circle means that the proton moves in a circular path around a central point, without any deviation or change in direction.

3. What factors affect the speed of a proton in orbit?

The speed of a proton in orbit is affected by the mass of the central object it is orbiting, the distance between the proton and the central object, and the gravitational force between the two objects.

4. How is the speed of a proton in orbit calculated?

The speed of a proton in orbit can be calculated using the formula v = √(GM/r), where v is the speed, G is the gravitational constant, M is the mass of the central object, and r is the distance between the proton and the central object.

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

The speed of a proton in orbit depends on the specific conditions of the orbit, such as the mass of the central object and the distance between the objects. However, for a proton to orbit in an exact circle, its speed would need to be precisely calculated using the formula mentioned in question 4.

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